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Distribution

Distribution, in economics, refers to the division of the aggregate output or income generated by production among the contributing factors—primarily labor, capital, land, and entrepreneurship—typically through market-determined returns such as wages, profits, interest, and rents.^[1]^[2] This process contrasts with production, which creates value, and consumption, which utilizes it, forming one of the core triads in classical economic analysis.^[2] The theory of distribution examines how these shares are determined, with neoclassical approaches emphasizing marginal productivity theory—wherein each factor receives a return equal to its marginal contribution to output under competitive conditions—while alternative views, such as those rooted in bargaining power or institutional factors, highlight influences like labor unions, technological change, and policy interventions.^[3] Empirical studies link distribution patterns to macroeconomic outcomes, including growth and investment, often finding that more even distributions correlate with stability but that incentives tied to unequal returns drive innovation and capital accumulation in market economies.^[4] Controversies persist over whether observed inequalities in distribution—such as power-law tails in income and wealth data—reflect efficient resource allocation or market failures requiring redistribution, with causal evidence suggesting that policies distorting marginal returns can reduce overall output despite short-term equity gains.^[3]^[5] Academic discourse on these issues frequently exhibits a bias toward interventionist solutions, underweighting empirical demonstrations of growth-eroding effects from excessive equalization efforts.^[4]

Philosophical Foundations

Distributive Justice Theories

Distributive justice theories address the moral principles for allocating scarce resources, opportunities, and burdens within a society, often debating whether distributions should prioritize equality, merit, need, or historical entitlement. These theories derive from first-principles considerations of human agency, productivity, and voluntary interactions, positing that just allocations align with causal contributions to value creation rather than imposed patterns. Key frameworks include merit-based proportionality, as articulated by Aristotle; outcome-oriented egalitarianism, as in John Rawls's difference principle; and entitlement-based holdings, as proposed by Robert Nozick. Empirical observations challenge rigid equality mandates, revealing that deviations from incentive-aligned distributions can undermine production and prosperity.^[6] Aristotle, in his Nicomachean Ethics, conceived distributive justice as geometric proportionality, wherein goods are allocated according to individuals' merit or contribution to the common good, such as virtue, effort, or societal role. This rejects arithmetic equality, arguing that treating unequals equally is unjust; instead, rewards must scale with desert to reflect causal inputs into collective welfare. For instance, in a polity, offices and honors go to those whose excellence merits them, preserving incentives for excellence.^[6]^[7] John Rawls, in A Theory of Justice (1971), advanced a contractualist approach where rational agents behind a "veil of ignorance"—unaware of their own talents, position, or preferences—select principles maximizing the position of the worst-off, yielding equal basic liberties and the difference principle permitting inequalities only if they benefit the least advantaged. This favors redistribution to equalize outcomes ex post, prioritizing need over desert. However, critics note its abstraction from real causal processes, as veil-derived rules ignore how ignorance-mandated transfers can distort incentives; empirical studies indicate that high redistribution correlates with reduced investment and slower growth by weakening work and innovation motives.^[8]^[9] Nozick's entitlement theory, outlined in Anarchy, State, and Utopia (1974), rejects patterned distributions like Rawls's, asserting justice in holdings if assets were acquired through just initial appropriation (without worsening others' positions) and transferred voluntarily, without regard to resulting inequalities. Rectification applies for historical injustices, but ongoing redistribution violates entitlements akin to forced labor. This aligns with causal realism, as distributions emerge endogenously from productive actions and exchanges, fostering prosperity; historical evidence supports this, with West Germany's market-oriented policies yielding GDP per capita roughly double East Germany's by 1989, despite similar starting points post-World War II, as command-style equalization suppressed incentives and output.^[10]^[11]^[12]

Historical and Ethical Debates

In ancient Greek philosophy, Plato's Republic (c. 375 BCE) envisioned a just society where the ruling guardians held property in common, eschewing private ownership to prevent corruption and ensure communal welfare, prioritizing outcome equality among the elite class over individual acquisition.^[13] This model subordinated personal shares to the state's hierarchical needs, with guardians receiving fixed provisions rather than accumulations based on merit or effort, reflecting an ethical tension between enforced uniformity and potential incentives for excellence.^[14] Medieval scholastic thinkers, particularly Thomas Aquinas in Summa Theologica (1265–1274), advanced a concept of justum pretium (just price) as an estimate approximating the good's intrinsic value, derived from production costs, labor expended, and communal utility, rather than arbitrary fiat or equal outcomes.^[15] Aquinas argued that prices deviating significantly from this estimate constituted usury or fraud, emphasizing procedural fairness in voluntary exchanges over redistributive mandates, though he allowed market fluctuations to influence the estimate without mathematical rigidity.^[16] This framework critiqued exploitative feudal distributions by tying justice to objective effort and mutual consent, countering both monopolistic hoarding and forced equalization. The Enlightenment marked a shift toward process-oriented ethics, as John Locke in Two Treatises of Government (1689) posited that property rights arise from labor mixing with unowned resources, legitimizing acquisition through individual effort while condemning feudal entitlements as violations of natural liberty absent consent or productivity.^[17] Locke's labor theory critiqued inherited or coercive distributions—prevalent in feudal systems—as unjust enclosures of the commons without compensatory improvement, favoring procedural fairness via voluntary industry over egalitarian outcomes that ignore differential contributions.^[18] In the 20th century, Friedrich Hayek's "The Use of Knowledge in Society" (1945) highlighted the epistemic limits of central planning, arguing that dispersed, tacit knowledge renders outcome-focused allocations inefficient, as planners lack price signals to coordinate resources effectively, leading to misdistributed scarcity.^[19] Contrasting this, Karl Marx's surplus value theory in Capital (1867) framed unequal distributions as inherent capitalist exploitation, where workers produce value exceeding wages, necessitating revolutionary equalization; yet empirical outcomes in socialist states like the Soviet Union (1922–1991) demonstrated chronic shortages, famines (e.g., Holodomor 1932–1933 killing millions), and growth lags versus market economies, underscoring causal failures in overriding decentralized incentives.^[20] These debates reveal persistent ethical friction: egalitarian pursuits often falter against procedural mechanisms that harness individual agency and information, as evidenced by the superior resource coordination in voluntary systems.^[21]

Mathematics and Probability

Probability Distributions

A probability distribution specifies the probabilities of outcomes for a random variable, serving as a foundational tool for modeling uncertainty in empirical phenomena. It adheres to the Kolmogorov axioms of probability, which posit that probabilities are non-negative real numbers, the probability of the entire sample space equals 1, and for any countable collection of mutually exclusive events, the probability of their union equals the sum of their individual probabilities.^[22] These axioms ensure distributions capture verifiable likelihoods without interpretive overlays, enabling derivations of moments like expectation and variance from first principles. For discrete random variables taking countable values, the distribution is defined by the probability mass function p(x) = P(X = x), where p(x) \geq 0 and \sum_x p(x) = 1.^[23] The Poisson distribution exemplifies this for counting rare events, such as defects in manufacturing, with probability mass p(k; \lambda) = \frac{\lambda^k e^{-\lambda}}{k!} for k = 0, 1, 2, \dots, where \lambda > 0 is the expected number of occurrences in the interval; it arises as the limit of binomial distributions under low probability and high trials.^[24] For continuous random variables over uncountable domains, the distribution uses the probability density function f(x), where f(x) \geq 0, \int_{-\infty}^{\infty} f(x) \, dx = 1, and P(a \leq X \leq b) = \int_a^b f(x) \, dx.^[25] The normal distribution, with density f(x; \mu, \sigma^2) = \frac{1}{\sqrt{2\pi \sigma^2}} \exp\left( -\frac{(x - \mu)^2}{2\sigma^2} \right), models symmetric phenomena around mean \mu with variance \sigma^2 > 0; its properties include equality of mean, median, and mode, and finite moments derivable from the density.^[26] The central limit theorem asserts that if X_1, X_2, \dots, X_n are independent and identically distributed with finite mean \mu and variance \sigma^2 > 0, then the standardized sum Z_n = \frac{\sum_{i=1}^n X_i - n\mu}{\sigma \sqrt{n}} converges in distribution to the standard normal as n \to \infty, justifying normal approximations for aggregates of independent trials in data analysis.^[27] Expectation and variance, E[X] = \int x f(x) \, dx or \sum x p(x), and \mathrm{Var}(X) = E[X^2] - (E[X])^2, quantify central tendency and spread, respectively, directly from the distribution without assuming underlying causality beyond the axioms.^[25]^[23]

Properties and Analytical Tools

The moments of a probability distribution serve as empirical summaries of its central tendency, dispersion, asymmetry, and tail behavior. The first raw moment defines the mean, \mu = E[X], representing the expected value. The second central moment is the variance, \sigma^2 = E[(X - \mu)^2], quantifying spread around the mean. Skewness, the third standardized moment \gamma_1 = E[(X - \mu)^3]/\sigma^3, measures asymmetry, with positive values indicating right-skewed tails and negative values left-skewed. Kurtosis, often excess kurtosis as the fourth standardized moment \gamma_2 = \{E[(X - \mu)^4]/\sigma^4\} - 3, assesses tail heaviness relative to a normal distribution, where values exceeding zero suggest leptokurtosis.^[28]^[29] While moments facilitate comparison across distributions, over-reliance on them presumes stationarity and often symmetry, assumptions invalidated in non-stationary data exhibiting trends, heteroscedasticity, or structural breaks, which can yield spurious correlations and unreliable inferences under traditional parametric models.^[30]^[31] Transformations such as the cumulative distribution function (CDF), F(x) = P(X \leq x), map random variables to uniform probabilities on [0,1], enabling probability inversion and standardization across distributions; it is non-decreasing, right-continuous, with \lim_{x \to -\infty} F(x) = 0 and \lim_{x \to \infty} F(x) = 1. The quantile function, Q(p) = \inf\{x : F(x) \geq p\} for p \in (0,1), inverts the CDF to yield values at specified probabilities, supporting robust estimation and simulation without density assumptions./03:_Distributions/3.06:_Distribution_and_Quantile_Functions) Sampling distributions describe the variability of estimators across repeated samples, underpinning hypothesis testing and prediction; for instance, the central limit theorem approximates the distribution of sample means as normal for large samples, facilitating inference. Confidence intervals, such as those for the mean using \bar{X} \pm t_{n-1, \alpha/2} \cdot s/\sqrt{n} under normality, quantify estimation uncertainty based on this variability. Bootstrap methods, developed by Bradley Efron in 1979, approximate sampling distributions non-parametrically via resampling with replacement from the data, generating empirical percentiles for bias-corrected intervals that validate results without assuming underlying forms, particularly useful for complex or small-sample scenarios.^[32]^[33]

Natural and Physical Sciences

Distributions in Physics and Chemistry

In statistical mechanics, the Boltzmann distribution describes the equilibrium occupation probabilities of discrete energy states in a classical system at temperature T, given by P_i = \frac{e^{-E_i / [kT](/page/KT)}}{[Z](/page/Z)}, where E_i is the energy of state i, k is Boltzmann's constant, and Z is the partition function ensuring normalization.^[34] This form emerges from the principle of maximizing the system's entropy S = -[k](/page/K) \sum p_i \ln p_i subject to constraints of fixed total probability and average energy, reflecting the causal tendency toward states that balance microscopic reversibility and macroscopic uniformity under thermal constraints.^[35] Ludwig Boltzmann formalized this in the 1870s through his H-theorem, linking it to molecular chaos assumptions in kinetic theory, though later critiques highlighted irreversibility paradoxes resolved via ergodicity.^[36] In quantum systems, distributions account for particle indistinguishability and exchange symmetry. For fermions (particles with half-integer spin obeying the Pauli exclusion principle), the Fermi-Dirac distribution governs occupation numbers: f(E) = \frac{1}{e^{(E - \mu)/kT} + 1}, where \mu is the chemical potential, preventing multiple occupancy of states and explaining electron degeneracy pressure in white dwarfs and metals.^[37] Enrico Fermi and Paul Dirac derived this in 1926 from quantum statistics, verified empirically through specific heat anomalies in metals at low temperatures and photoemission spectroscopy confirming filled Fermi seas up to ~10 eV binding energies.^[38] For bosons (integer-spin particles), the Bose-Einstein distribution f(E) = \frac{1}{e^{(E - \mu)/kT} - 1} allows macroscopic occupation of ground states below a critical temperature, leading to Bose-Einstein condensation (BEC) first observed in 1995 with ultracold rubidium-87 atoms at 170 nK, where ~40% of atoms condensed into the ground state.^[39] In superconductors, Bardeen-Cooper-Schrieffer theory (1957) treats electron pairs as composite bosons that condense, enabling zero-resistance current flow verified in lead at 7.2 K.^[40] The Maxwell-Boltzmann distribution extends to continuous velocities in ideal gases, with the speed distribution f(v) = 4\pi v^2 \left(\frac{m}{2\pi kT}\right)^{3/2} e^{-mv^2 / 2kT}, where m is molecular mass, derived by James Clerk Maxwell in 1860 from collision invariants and later connected to Boltzmann's work.^[41] In chemical kinetics, it underpins collision theory, where reaction rates depend on the fraction of molecules exceeding activation energies E_a, approximated as e^{-E_a / kT}, explaining Arrhenius behavior observed in gas-phase reactions like H2 + I2 at 700 K with rate constants scaling exponentially.^[42] Deviations arise in non-equilibrium conditions, such as plasmas, where electron energy distributions often follow kappa distributions f(\epsilon) \propto (1 + \epsilon / \kappa \theta^2)^{-\kappa -1} with \kappa \approx 2-6, reflecting suprathermal tails from wave-particle interactions rather than collisional equilibration, as measured in solar wind probes showing effective temperatures 10-100 times kinetic values.^[43] ^[44] These causal deviations, driven by electric fields and low collision rates (~10^{-6} s^{-1} in space plasmas), contrast equilibrium assumptions and inform fusion reactor designs where non-Maxwellian tails enhance cross-sections by factors of 2-5.^[45]

Distributions in Biology and Ecology

In biology and ecology, distributions refer to the spatial and temporal patterns of species, populations, or genetic traits, influenced by abiotic factors like climate and soil, biotic interactions such as competition and predation, and evolutionary processes including natural selection and genetic drift. These patterns are modeled to test causal mechanisms, with empirical data from field observations and geographic information systems (GIS) enabling validation against predictions. For instance, species distribution models (SDMs) integrate occurrence data with environmental variables to forecast ranges, rooted in niche theory which posits that species occupy specific environmental conditions where fitness is maximized.^[46]^[47] Species distribution models, such as those based on maximum entropy (MaxEnt), predict geographic ranges by correlating presence records with variables like temperature, precipitation, and habitat suitability, often validated through independent datasets or cross-validation techniques using GIS layers. Empirical tests reveal that while correlative SDMs perform well for broad-scale predictions under current climates, they overestimate ranges when biotic interactions like competition or dispersal barriers are omitted, as demonstrated in studies of European plant species where model accuracy dropped by up to 30% without competition data. Niche theory underpins these models by assuming fundamental niches (physiological tolerances) are constrained by realized niches (actual distributions) shaped by interspecific interactions, with causal inference strengthened by experiments manipulating environmental gradients.^[46]^[48] Genetic distributions within populations are characterized by allele frequency patterns, which under random mating, large population size, and no selection approximate Hardy-Weinberg equilibrium, where genotype frequencies stabilize as p^2 + 2pq + q^2 = 1 for a biallelic locus with allele frequencies p and q. Deviations from this equilibrium signal evolutionary forces: excess homozygotes indicate inbreeding or Wahlund effect from population substructure, while heterozygote deficits may arise from selection against hybrids, as observed in genomic studies of human populations where large-scale sequencing data showed HWE violations in 5-10% of loci due to drift in isolated groups. Population genetics analyses, such as chi-square tests on empirical allele counts from thousands of SNPs, quantify these disruptions, enabling inference of migration rates or selection coefficients from frequency clines across spatial gradients.^[49]^[50] Temporal distributions, such as age or size structures, reflect demographic processes and are projected using Leslie matrices, which incorporate age-specific survival (l_x) and fertility (m_x) rates to forecast population vectors over time via \mathbf{n}_{t+1} = \mathbf{L} \mathbf{n}_t, where \mathbf{L} is the projection matrix and \mathbf{n}_t the age-class abundances at time t. In ecological applications, these models have projected growth for species like Soay sheep, revealing stable age distributions under fluctuating environments, with the dominant eigenvalue \lambda indicating long-term growth rate. However, projections often overemphasize density-dependent regulation via resource competition, underincorporating predation's variable effects; studies of mammalian populations show that predator-induced mortality is frequently compensatory rather than additive at high densities, leading to biased forecasts when predation data is sparse, as evidenced by forecasting errors exceeding 20% in models ignoring top-down controls. Causal realism demands integrating predation time-series data to distinguish density-dependence from extrinsic drivers, avoiding overreliance on bottom-up assumptions unsubstantiated by longitudinal censuses.^[51]^[52]^[53]

Economics

Allocation of Goods and Resources

In market economies, the allocation of goods and resources occurs through distribution channels that facilitate the movement of products from producers to consumers via voluntary exchanges, emphasizing efficiency over coercive directives. These channels typically include indirect pathways involving intermediaries such as wholesalers, who purchase in bulk from manufacturers and supply retailers, and retailers, who sell directly to end-users, thereby reducing transaction costs and enabling specialization.^[54] Direct-to-consumer models, where producers sell straight to buyers, bypass intermediaries to capture higher margins but require robust logistics, as seen in sectors like e-commerce where such approaches have expanded access while optimizing inventory turnover.^[55] Price signals in supply-and-demand dynamics guide this allocation by adjusting quantities and directing resources to highest-value uses, with empirical studies showing that undistorted prices enhance productivity and prevent misallocation of factors like capital and labor.^[56] Competition among channel participants enforces these signals, curbing monopolistic pricing and ensuring surplus moves efficiently; for instance, the 1911 U.S. Supreme Court breakup of Standard Oil under the Sherman Antitrust Act dissolved its 90% market dominance, leading to subsequent entry of rivals and price stabilization in refined petroleum, underscoring how antitrust intervention can restore competitive pressures absent in unchecked consolidation.^[57]^[58] This emergent process arises from secure property rights enabling trade, which incentivizes agents to minimize waste through decentralized decisions rather than top-down mandates. In contrast, centralized planning in systems like the Soviet Union generated chronic shortages, as planners lacked localized knowledge and price feedback, resulting in overproduction of heavy industry goods and under-supply of consumer items—evidenced by persistent queues and black markets from the 1960s onward, with empirical models confirming shortages stemmed from repressed inflation and allocation rigidities rather than external factors.^[59] Property rights-backed markets thus achieve superior resource matching, as voluntary trades align supply with revealed preferences, avoiding the inefficiencies of command economies where misaligned incentives led to GDP growth stagnation by the 1970s.^[60]

Income and Wealth Distribution

Income distribution refers to the allocation of earnings from labor and capital across individuals or households, while wealth distribution encompasses the spread of net assets such as savings, property, and investments. These patterns are commonly analyzed using the Lorenz curve, which plots the cumulative share of income or wealth held by the bottom x% of the population against the line of perfect equality, and the Gini coefficient, derived as the ratio of the area between the Lorenz curve and the equality line to the total area under the equality line, ranging from 0 (perfect equality) to 1 (perfect inequality).^[61] For instance, a Gini of 0.3 indicates moderate inequality, as seen in many middle-income economies.^[61] Globally, the Gini coefficient for income rose from approximately 0.60 in 1820 to a peak of 0.72 around 2000 before declining to 0.67 by 2020, driven primarily by rapid economic catch-up in Asia through expanded trade and technological diffusion that lifted billions from poverty without proportional equalization.^[62] Post-1980s liberalization in countries like China and India facilitated this trend: China's extreme poverty rate fell from 88% in 1981 to under 1% by 2015 amid Gini coefficients rising from about 0.30 in the early 1980s to a peak near 0.49 in 2008 before stabilizing around 0.38 by 2022, reflecting structural shifts toward market-oriented growth.^[63]^[64] Similarly, India's consumption-based Gini hovered around 0.35-0.40 during periods of accelerated GDP growth, correlating with poverty reduction from 45% in 1993 to about 11% by 2022-23, as entrepreneurship and skill acquisition outpaced redistribution efforts.^[65]^[66] These patterns align with the Kuznets curve hypothesis, where inequality rises during early industrialization due to differential returns to urban migration and capital-intensive sectors but accompanies absolute gains for the poor via overall expansion.^[67] Empirical determinants of these distributions emphasize productivity variations rooted in human capital accumulation—such as education and skills—and exogenous technological progress, as formalized in the augmented Solow growth model, which decomposes output per worker into contributions from physical capital, human capital stocks, population dynamics, and total factor productivity growth.^[68] In this framework, long-run income disparities arise not from zero-sum transfers but from differential investments yielding higher marginal products, with cross-country evidence showing that economies prioritizing human capital formation, like post-reform East Asia, exhibit elevated Gini levels during high-growth phases yet achieve sustained poverty declines through compounded efficiency gains.^[69] Institutions supporting secure property rights and open markets amplify these effects by incentivizing innovation over rent-seeking, explaining why inequality in dynamic economies like China and India has coincided with broader welfare improvements rather than systemic harm.^[70] Wealth distributions tend to be more skewed than income ones, with global top 10% wealth shares exceeding 80% in many nations, as assets compound returns from underlying productivity differences.^[62]

Theoretical Foundations and Empirical Critiques

Marginal productivity theory posits that wages reflect the marginal revenue product of labor, determined by workers' contributions to output under competitive conditions.^[71] Empirical tests using firm-level data, such as manufacturing plants in Chile, reveal that wages approximate marginal products after controlling for skill heterogeneity and market imperfections, though moderate deviations occur due to monopsony power or bargaining.^[71] Labor market regressions across OECD economies from 1960–2019 further demonstrate a positive long-run relationship between labor productivity growth and real wage increases, supporting the theory's core mechanism despite assumptions of perfect competition being relaxed in imperfect markets.^[72] Thomas Piketty's argument that returns on capital (r) persistently exceed economic growth (g), driving inevitable inequality, has faced empirical scrutiny for overlooking intangible assets and entrepreneurial risk.^[73] Critics note that Piketty's data underweights human capital accumulation and innovation-driven intangibles, which elevate effective returns in dynamic economies, while aggregating returns ignores losses from entrepreneurial failure.^[74] Variations in r-g observed across policies—such as stagnation in high-tax, low-growth European regimes post-1970s—contradict claims of inexorable divergence, as fiscal burdens on capital suppress returns without addressing underlying productivity drivers.^[73] Debates on redistribution highlight causal evidence favoring structural reforms over direct transfers for sustained income growth. Randomized controlled trials in developing countries, including property titling programs in Peru and India, show formalizing ownership boosts investment, entrepreneurship, and household incomes by 20–30% more than equivalent cash handouts, as secure rights enable credit access and asset utilization. In contrast, unconditional cash transfers yield short-term consumption gains but limited long-run poverty escape without complementary incentives.^[75] Historical cases like Venezuela's 2013–2020 collapse, where aggressive redistribution via nationalizations and subsidies amid oil dependency led to 99% private sector contraction and hyperinflation exceeding 1 million percent by 2018, illustrate how eroding property rights and incentives precipitates output falls outweighing any transient equity.^[76]

Computing and Information Technology

Software and Digital Content Distribution

Software distribution encompasses centralized platforms such as app stores and package managers, alongside decentralized approaches like peer-to-peer networks and content delivery networks (CDNs). The Apple App Store, launched on July 10, 2008, pioneered centralized mobile software dissemination by enabling developers to distribute applications through a vetted ecosystem, achieving over 2 billion downloads within its first year. Similarly, Google's Android Market (rebranded Google Play in 2012) facilitated billions of app installations by 2013, prioritizing accessibility over stringent review processes compared to Apple's model. These platforms enforce proprietary control, limiting redistribution but ensuring revenue models via commissions, typically 30%. In contrast, decentralized methods like BitTorrent, introduced in 2001 by Bram Cohen, enable direct peer-to-peer file sharing, reducing reliance on single servers and distributing load across users for scalable dissemination of software binaries.^[77] Digital content distribution, including media files and updates, leverages CDNs for efficient global delivery by caching content on edge servers proximate to users, thereby minimizing latency—often reducing load times by up to 50% in streaming applications.^[78] Pioneered by Akamai in 1998, CDNs handle massive scale, such as Netflix's traffic, which comprised 37% of U.S. internet usage in 2019 via optimized routing. Peer-to-peer protocols complement this by decentralizing bandwidth, as in BitTorrent swarms where upload contributions from peers cut central server costs by 60-80% in high-demand scenarios, though variable peer quality can introduce inconsistencies.^[78] Hybrid models, integrating P2P with CDNs, further enhance efficiency, lowering latency in live streaming by dynamically sourcing segments from nearby peers.^[79] Open-source licensing profoundly influences distribution dynamics, balancing accessibility against control. The GNU General Public License (GPL), first published in 1989 by the Free Software Foundation, enforces copyleft—requiring derivative works to remain open-source—which restricts proprietary integration but promotes communal development, as seen in the Linux kernel's widespread adoption in servers (over 90% market share in 2023). Conversely, permissive licenses like the MIT License, originating in 1988 at the Massachusetts Institute of Technology, allow unrestricted use including in closed-source products, correlating with higher adoption: GitHub data from 2022 indicates MIT and Apache 2.0 comprising over 50% of licenses, far exceeding GPL's share, due to developer preference for flexibility in commercial ecosystems.^[80] This permissiveness empirically boosts repository forks and stars on GitHub, with MIT-licensed projects averaging 20-30% more contributors than GPL equivalents in comparable domains.^[80] Proprietary models, by contrast, retain intellectual property via end-user license agreements, enabling controlled monetization but potentially stifling innovation through barriers to modification. Security remains paramount in these channels, as distribution vectors serve as entry points for malware. Supply chain attacks, such as the 2020 SolarWinds breach affecting 18,000 organizations, exploited trusted update mechanisms to inject malicious code.^[81] Mitigation relies on cryptographic techniques: file hashing verifies integrity by comparing checksums (e.g., SHA-256) against known values, detecting tampering during P2P transfers or downloads. Code signing, using digital certificates from authorities like DigiCert, authenticates executables and prevents unsigned malware execution on platforms like Windows and macOS, reducing infection risks by ensuring provenance—Microsoft reports over 99% of blocked malware lacks valid signatures.^[82] In open-source repositories, these practices, combined with vulnerability scanning in tools like GitHub Dependabot, address risks amplified by decentralized access, though proprietary vetting in app stores provides an additional layer of centralized scrutiny.^[83]

Data Distributions and Algorithms

In machine learning, data distributions refer to the probability patterns underlying datasets, which algorithms must handle to ensure reliable inference and prediction. Distribution shifts, such as covariate shift where the input feature distribution changes between training and test data while the conditional label distribution remains constant, pose challenges to model generalization.^[84] Domain adaptation techniques mitigate these by aligning source and target distributions, often through methods like importance weighting or adversarial training.^[85] In image recognition tasks, benchmarks demonstrate the efficacy of these approaches; for instance, unsupervised domain adaptation on datasets like Office-31 or VisDA improves classification accuracy by 10-20% under covariate shifts induced by domain differences such as synthetic versus real images.^[86] Similarly, covariate shift adaptation enhances robustness to common corruptions like noise or blur in CIFAR-10-C, boosting recognition performance without retraining on target data.^[87] These methods rely on empirical risk minimization adjusted for shift estimation, grounded in the assumption that label shifts are absent or separately modeled. Sampling algorithms approximate complex posterior distributions in Bayesian inference, where direct computation is intractable. Markov Chain Monte Carlo (MCMC) methods, including the Metropolis-Hastings algorithm, generate sequences of samples that converge to the target distribution under ergodicity conditions—irreducibility, aperiodicity, and positive Harris recurrence.^[88] Convergence theorems, such as those extending the central limit theorem to Markov chains, ensure that sample averages approach expectation values as chain length increases, provided finite variance holds.^[89] In practice, diagnostics like Gelman-Rubin statistics assess chain convergence by comparing intra- and inter-chain variances, with values below 1.1 indicating stability after burn-in periods of thousands of iterations for high-dimensional models.^[90] These guarantees enable MCMC for tasks like posterior inference in Gaussian processes, where exact sampling fails. Big data often exhibits skewed distributions, particularly power-laws where event frequencies follow P(k) \propto k^{-\alpha} with \alpha > 1, leading to heavy tails and challenges in processing rare high-impact events.^[91] In web traffic, Zipf's law—a discrete power-law variant—manifests as site visit ranks inversely proportional to frequency, observed in AOL query logs where top sites capture disproportionate shares, though deviations occur for extreme ranks due to finite data effects.^[92] Such skews in network data necessitate specialized algorithms like reservoir sampling or heavy-hitter sketches to handle imbalance without uniform assumptions.^[93]

Business and Logistics

Supply Chain and Commercial Distribution

Commercial distribution encompasses the operational movement of physical goods through supply chains, from manufacturing facilities to end-users, involving coordinated logistics to ensure timely delivery while minimizing costs. Key stages include manufacturing or assembly, warehousing for inventory storage, transportation via trucks, ships, or rail, and final distribution to retailers or consumers, often supported by order processing and materials handling.^[94] These processes rely on inventory control to balance supply with demand, preventing stockouts or excess holding.^[95] Inventory models such as the Economic Order Quantity (EOQ) optimize order sizes to minimize combined ordering and holding costs, calculated via the formula EOQ = √(2DS/H), where D is annual demand, S is ordering cost per order, and H is holding cost per unit.^[96] Just-In-Time (JIT) systems further enhance efficiency by reducing inventory levels through precise supplier coordination, lowering carrying costs by up to 50% in implementations like Toyota's production model and improving cash flow by aligning production closely with demand.^[97]^[98] Market incentives, driven by competitive pressures, encourage adoption of these models to cut waste and boost responsiveness. Global supply chains leverage comparative advantage, where countries specialize in production based on relative efficiencies, leading to overall trade volume growth and productivity gains; for instance, WTO analyses indicate that open trade has historically increased global efficiency by enabling resource allocation to high-output sectors.^[99]^[100] Empirical evidence from trade liberalization shows manufacturing sectors benefiting from $3.5 billion in added growth in some economies due to specialized imports.^[101] However, such interdependence introduces risks, as seen in the 2018-2019 U.S.-China trade war, where tariffs on $380 billion in goods raised supply chain costs, with U.S. importers bearing the full incidence and aggregate real income falling by approximately $1.4 billion monthly.^[102]^[103] To build resilience, firms diversify suppliers and adopt multi-sourcing strategies, reducing single-point failures amid disruptions like tariffs or pandemics, with market incentives favoring agile networks that balance cost competitiveness against vulnerability.^[104]^[105] Post-2018 shifts, such as increased Mexican exports to the U.S. by 4.2% per 25 percentage point tariff hike on China, illustrate how competitive relocation enhances chain robustness without government mandates.^[106] These adaptations underscore causal links between policy-induced shocks and private-sector responses prioritizing efficiency and continuity.

Modern Trends and Challenges

Following the COVID-19 disruptions that caused global supply chain shortages—such as semiconductor deficits peaking in 2021 and persisting into 2023—businesses have shifted toward nearshoring and diversification to bolster resilience.^[107] Nearshoring to proximate regions like Mexico enabled quicker recovery from pandemic-induced halts, reducing lead times and exposure to geopolitical risks compared to far-off sourcing.^[108] By 2024, surveys of supply chain leaders showed 60% prioritizing multi-sourcing strategies, with the Manufacturing Supplier Deliveries Index improving to 48.9 in April from 47 in late 2023, signaling reduced but lingering vulnerabilities.^[109]^[107] Advancements in AI-driven predictive analytics have accelerated since 2020, enabling precise demand forecasting by analyzing historical data, market trends, and external variables like weather or geopolitics.^[110] The global predictive analytics market for supply chains is forecasted to expand from $17.07 billion in 2024 to $20.77 billion in 2025, reflecting a 21.6% compound annual growth rate, with applications cutting forecast errors by 20-50%.^[111]^[112] Complementing this, warehouse automation via autonomous mobile robots (AMRs) integrated with IoT has gained traction for 2025, enhancing picking accuracy and throughput while minimizing human error; projections indicate 70% of logistics mobile robots will incorporate IoT by 2026 for real-time coordination.^[113]^[114] Sustainability initiatives in distribution emphasize route optimization and modal shifts to lower carbon emissions, with green supply chain management (GSCM) practices demonstrably reducing waste and footprints through efficient resource allocation.^[115] Yet empirical analyses reveal trade-offs, where aggressive GSCM adoption correlates with diminished profitability due to higher upfront investments in eco-friendly technologies and processes, challenging claims of unalloyed cost savings.^[116] Regulatory green mandates, such as stringent emissions targets, often elevate logistics costs—potentially by 10-20% in compliant networks—while yielding marginal global impact, as major emission sources in developing economies remain unaddressed by localized optimizations.^[116]^[117]

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Distribution is the species of Exchange by which produce is divided between the parties who have contributed to its production.
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[PDF] THE DISTRIBUTION OF WEALTH *
This chapter is concerned with the distribution of personal wealth, which usually refers to the material assets that can be sold in the marketpace, ...
[6]
Nicomachean Ethics by Aristotle - The Internet Classics Archive
This is found among men who share their life with a view to selfsufficiency, men who are free and either proportionately or arithmetically equal, so that ...
[7]
[PDF] Aristotle's Conception of Justice - NDLScholarship
" There exist two kinds of Equality (or. Justice): namely, "strict Equality" and "proportionate. Equality," for there are certain claims which can only be.
[8]
John Rawls on Justice
Sep 3, 2002 · To say that we are behind a Veil of Ignorance is to say we do not know the following sorts of things: our sex, race, physical handicaps, ...<|separator|>
[9]
Growth effects of inequality and redistribution - ScienceDirect.com
Public redistribution, measured as the difference between Ginis of market and net income, hampers growth via lower investment and increased fertility. Yet, ...
[10]
ROBERT NOZICK'S ENTITLEMENT THEORY OF JUSTICE
Jul 20, 2023 · ROBERT NOZICK'S ENTITLEMENT THEORY OF JUSTICE: A CRITICAL ANALYSIS ... entitled to the holding is entitled to the holding;; No one is ...
[11]
Comparing the Economic Growth of East Germany to West ... - FEE.org
The eastern part of Germany was actually richer than the western part prior to World War II. The entire country's economy was then destroyed by the war.
[12]
Former East Germany remains economically behind West
Nov 6, 2019 · Per-capita gross domestic product was €32,108 in the former East German states in 2018, compared with €42,971 in the former West German states.
[13]
Plato: The Republic | Internet Encyclopedia of Philosophy
Socrates proceeds to discuss the living and housing conditions of the guardians: they will not have private property, they will have little privacy, they will ...
[14]
https://www.philosophypages.com/hy/2g.htm
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Thomas Aquinas on the Just Price - Public Discourse
Mar 19, 2019 · Thomas admits that the just price “is not fixed with mathematical precision but depends on a kind of estimate.” It varies over time and place, ...
[16]
Scholastic Economics: Thomistic Value Theory - Acton Institute
Jul 20, 2010 · Saint Thomas Aquinas' writings in value theory entail the proposition that the basis of value of an economic good is the amount of human labor expended in ...
[17]
Locke and Labour - Online Library of Liberty
Sep 14, 2021 · Locke notoriously invoked the idea that resources are originally acquired through their admixture with labour.
[18]
[PDF] JOHN LOCKE AND THE LABOR THEORY OF VALUE - Mises Institute
Such a theory tries to establish an exclusive relationship between the effort (or time) of the laborer and relative price of the commodity he produces. The most ...
[19]
Marxism - Econlib
But Marx failed as well. By the late nineteenth century, the economics ... But if comprehensive socialist planning fails to work in practice—if, indeed ...Missing: empirical | Show results with:empirical<|separator|>
[20]
Why Marx Was Wrong about Workers and Wages - Mises Institute
Sep 14, 2024 · However, as Mises and other Austrians have noted, Marx failed both at understanding the complexity of labor and subjective value theories.Missing: empirical | Show results with:empirical
[21]
Centrally Planned Economy: Features, Pros & Cons, and Examples
One major critique, associated with Friedrich Hayek, is that central planners cannot efficiently respond to supply and demand. In a market economy, businesses ...<|separator|>
[22]
Kolmogorov axioms of probability - The Book of Statistical Proofs
Jul 30, 2021 · We introduce three axioms of probability: P(E)∈R,P(E)≥0,for all E∈E. (1) P(Ω)=1. (2) Third axiom: The probability of any countable sequence of disjoint (ie ...
[23]
3.1.3 Probability Mass Function (PMF)
Thus, the PMF is a probability measure that gives us probabilities of the possible values for a random variable. While the above notation is the standard ...
[24]
Poisson Distribution - an overview | ScienceDirect Topics
1 The Poisson distribution. The Poisson distribution is used to describe the distribution of rare events in a large population. For example, at any ...
[25]
14.1 - Probability Density Functions | STAT 414 - STAT ONLINE
A probability density function (p.d.f.) is a curve for continuous random variables, where the area under the curve represents probability. It is an integrable ...<|separator|>
[26]
Normal Distribution | Gaussian | Normal random variables | PDF
The normal distribution is very important, related to the Central Limit Theorem. A normal random variable is defined as X∼N(μ,σ2), where X is obtained by ...
[27]
Central Limit Theorem - Probability Course
It states that, under certain conditions, the sum of a large number of random variables is approximately normal.
[28]
Definitions of moments in probability and statistics - The DO Loop
Sep 28, 2022 · The mean is defined as the first raw moment. The variance is the second central moment. The skewness and kurtosis are the third and fourth ...
[29]
Moments and Moment Generating Functions - Milefoot
A common definition of skewness is the third moment about the mean, E((X−μ)3). A common definition of kurtosis is the fourth moment about the mean, E((X−μ)4).<|separator|>
[30]
Why non-stationary data cannot be analyzed?
Sep 3, 2013 · Non-stationary cannot be analyzed with traditional econometric techniques as in case of non-stationarity some basic model assupmtions are not met.
[31]
Why non stationarity is a problem in a time series data analysis?
Jun 4, 2020 · Using non-stationary time series data in financial models produces unreliable and spurious results and leads to poor understanding and ...
[32]
[PDF] Bootstrap confidence intervals Class 24, 18.05 - MIT Mathematics
The empirical bootstrap is a statistical technique popularized by Bradley Efron in 1979. Though remarkably simple to implement, the bootstrap would not be ...
[33]
[PDF] Introduction to Bootstrap Methods in Statistics
In other words, the sampling distribution of g(T) can be estimated, and an equal-tailed. (1 − a)100% confidence interval for g(0) can be formed, by the same ...
[34]
[PDF] Boltzmann Distribution and Partition Function - MIT OpenCourseWare
In these notes, we introduce the method of Lagrange multipliers and use it to derive the Boltzmann distribu- tion. From the Boltzmann distribution, ...
[35]
[PDF] Derivation of the Boltzmann Distribution - UF Physics
In order to simplify the numerical derivation, we will assume that the energy E of any individual particle is restricted to one or another of the values 0, DE, ...
[36]
[PDF] 6-1 CHAPTER 6 BOLTZMANN'S H-THEOREM In the latter part of ...
In the latter part of the nineteenth century, Ludwig Boltzmann almost single-handedly established the field now known as statistical mechanics. One of his ...
[37]
8.5: Applications of the Fermi-Dirac Distribution - Physics LibreTexts
May 27, 2024 · We now consider some applications of the Fermi-Dirac distribution (8.2.5). It is useful to start by examining the behavior of this function ...
[38]
[PDF] Lecture 13: Metals
This is known as the Fermi-Dirac distribution or Fermi function, f("). As T ! 0 the function approaches a step function where all the states below are occupied ...
[39]
[PDF] Lecture 12: Bose-Einstein Condensation
In the BCS theory, the superconductivity is explained through the condensation of pairs of electrons called cooper pairs. These pairs act like bosons and form a ...
[40]
Superconductivity of a Charged Ideal Bose Gas | Phys. Rev.
It is shown that an ideal gas of charged bosons exhibits the essential equilibrium features of a superconductor. The onset of Bose-Einstein condensation ...
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3.1.2: Maxwell-Boltzmann Distributions - Chemistry LibreTexts
Jul 7, 2024 · The Maxwell-Boltzmann equation, which forms the basis of the kinetic theory of gases, defines the distribution of speeds for a gas at a certain temperature.Introduction · Plotting the Maxwell... · Related Speed Expressions
[42]
[PDF] Applications of the Boltzmann distribution
Sep 14, 2021 · Foundations of Chemical Kinetics Lecture 3: Applications of the ... Maxwell-Boltzmann distribution of relative speeds: p(urel)durel ...
[43]
Unifying Kappa Distribution Models for Non-Equilibrium Space ...
Sep 9, 2025 · These distributions deviate from the canonical Maxwell-Boltzmann statistics and vary significantly in their interpretation of the temperature ...
[44]
[PDF] Non-equilibrium in low-temperature plasmas
Nov 22, 2016 · This paragraph deals with the effects of collisions on the deviation of electron distribution function from. Maxwellian behavior. A strong ...
[45]
Non-equilibrium statistical properties, path-dependent information ...
Nov 4, 2022 · Plasmas in fusion devices are volatile and constitute one of the prototypical examples of non-equilibrium systems1 involving large fluctuations.
[46]
Species distribution models and empirical test
Species distribution models (SDMs) estimate the geographical distribution of species although with several limitations due to sources of inaccuracy and ...
[47]
Species Distribution Models: Ecological Explanation and Prediction ...
Dec 1, 2009 · Species distribution models (SDMs) are numerical tools that combine observations of species occurrence or abundance with environmental ...
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Ecological niche modelling - ScienceDirect.com
Mar 25, 2024 · Ecological niche models are computational tools that relate observed species occurrence, abundance or biomass data with selected environmental variables.Missing: empirical GIS
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The Hardy-Weinberg Principle | Learn Science at Scitable - Nature
The Hardy-Weinberg theorem characterizes the distributions of genotype frequencies in populations that are not evolving, and is thus the fundamental null model ...
[50]
Hardy-Weinberg Equilibrium in the Large Scale Genomic ... - NIH
Mar 13, 2020 · Hardy-Weinberg Equilibrium (HWE) is used to estimate the number of homozygous and heterozygous variant carriers based on its allele frequency in populations ...
[51]
[PDF] Life Table and Population Projection Using the Leslie Matrix
A life table shows mortality rates by age. The Leslie Matrix uses fertility and survival rates to project future age distributions.
[52]
[PDF] FW662 Lecture 6 – Evidence of density dependence
Predation (broadly including disease, parasitism, parasitoids, and herbivory) is not always density dependent. For predators to cause top-down regulation via.
[53]
Ecological forecasts reveal limitations of common model selection ...
Jun 24, 2020 · In the present study, we evaluated how density dependence and numerous extrinsic factors (i.e., external processes that affect the species such ...
[54]
Distribution Channels: The Efficient Flow of Goods and Services
An indirect distribution channel relies on intermediaries such as wholesalers, retailers, and brokers to deliver products to consumers. This method helps ...
[55]
Direct vs. Indirect Distribution Channels - Inbound Logistics
Sep 15, 2024 · This article will provide a clear explanation of both direct and indirect distribution channels, breaking down their differences, benefits, and common uses.
[56]
Price distortion on market resource allocation efficiency
Price distortion cause production factors such as capital and labor to be employed at lower productivity, preventing effective allocation of resources to their ...
[57]
Standard Oil Co. of New Jersey v. United States (1911) | Wex | US Law
In this case, however, the Court found that Standard Oil of New Jersey's actions led to these consequences and therefore violated the Sherman Antitrust Act.
[58]
The Antitrust Legacy of Standard Oil in Today's World - JPT/SPE
Nov 1, 2021 · The antitrust legacy of Standard Oil, after the breakup of the company 110 years ago, continues to impact the American judicial system's treatment of antitrust ...
[59]
The Chronic Shortage Model of Centrally Planned Economies - jstor
The empirical evidence confirms the existence of chronic shortage. In each area further research would provide additional insights into the economics of. CPEs.
[60]
Technical change and the postwar slowdown in Soviet economic ...
Sep 26, 2023 · The existing studies usually find that technical change was very important in constraining the economic growth of the Soviet Union.
[61]
Measuring inequality: what is the Gini coefficient? - Our World in Data
Jun 30, 2023 · Gini coefficient = A / (A + B) The Lorenz curve is the “line of equality” where incomes are shared perfectly equally.
[62]
Global inequality from 1820 to now
In effect, the global Gini increased from 0.60 in 1820 to 0.72 in 1910, again 0.72 in 2000 and 0.67 in 2020 (see Figure 2.3). Note that the global inequality ...
[63]
Gini index - China - World Bank Open Data
Gini index - China. World Bank, Poverty and Inequality Platform. Data are based on primary household survey data obtained from government statistical agencies ...
[64]
GINI Index for China (SIPOVGINICHN) | FRED | St. Louis Fed
GINI Index for China (SIPOVGINICHN) ; 2022: 36.0 ; 2021: 35.7 ; 2020: 37.1 ; 2019: 38.2 ; 2018: 38.5.
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India - Poverty and Inequality Platform - World Bank
Poverty and Equity Briefs are two-page country summaries that provide an overview of recent developments in poverty reduction, along with the latest data of key ...
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What India Gini score says about economic welfarism and its success
Jul 10, 2025 · India's poverty rates have declined. According to NITI Aayog, poverty rates fell from 29.17 per cent in 2013-14 to 11.28 per cent in 2022-23 ...
[67]
[PDF] NBER WORKING PAPER SERIES IS THAT REALLY A KUZNETS ...
The path of income inequality in post-reform China has been widely interpreted as “China's Kuznets curve.” We show that the Kuznets growth model of structural ...
[68]
[PDF] Lecture 4, The Solow Growth Model and the Data - MIT Economics
Nov 8, 2022 · Solow's (1957) applied this framework to US data: a large part of the growth was due to technological progress. From early days, however, a ...Missing: inequality | Show results with:inequality
[69]
[PDF] This paper examines whether the Solow growth model is consistent ...
We find that accumulation of human capital is in fact correlated with saving and population growth. Including human-capital accumulation lowers the esti- mated ...
[70]
[PDF] solow and the states; capital accumulation, productivity and ...
the Solow growth model for the presence of human capital markedly improves its predictive performance in a cross-national study of economic growth. The flow ...Missing: determinants | Show results with:determinants
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An empirical test of marginal productivity theory | Request PDF
Aug 8, 2025 · Our empirical application using data on manufacturing plants in Chile suggest moderate deviations from marginal productivity theory which depend ...Abstract · References (40) · Recommended Publications
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[PDF] evidence from a panel of OECD economies over 1960-2019
This paper provides an empirical investigation of the relationship between labor productivity (LP), real wages (RW), and employment (EMP) in a panel of OCED ...
[73]
An Empirical Critique of Thomas Piketty's "Capital in the 21st Century"
A detailed examination of several of his core empirical claims, with particular attention to how they are utilized to support his core arguments.
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[PDF] Review and Critique of Piketty's Capital in the Twenty-First Century
Piketty may include the entrepreneurial effect in a high average return on capital, but that approach ignores the truly unique and personal catalyzing and ...Missing: intangible | Show results with:intangible
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[PDF] Using RCTs to Estimate Long-Run Impacts in Development ...
Most of these studies examine existing cash transfer, child health, or education interventions, and shed light on important theoretical questions such as the ...
[76]
Venezuela: Socialism, Hyperinflation, and Economic Collapse - AIER
Mar 1, 2017 · The redistribution policies of Chávez depended completely on revenue from Venezuela's state-owned oil industry. Private industry was strangled ...
[77]
A Brief History of P2P Content Distribution, in 10 Major Steps - Medium
Oct 25, 2017 · 6 - 2001 - Bittorrent Vuze (ex-Azureus) was the first BitTorrent client to migrate to a trackerless system by implementing a distributed hash ...Missing: software CDNs
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P2P for Content Distribution Networks (CDNs) - Comparitech
Apr 3, 2025 · P2P technology enhances CDN scalability by reducing infrastructure costs, optimizing bandwidth, improving delivery speed, and ensuring global content ...
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P2P Streaming: Benefits And How It Works | 2025 Guide - inoRain OTT
Feb 11, 2025 · P2P streaming reduces latency and buffering issues by distributing live video feeds efficiently among viewers rather than overloading a single ...How P2p Streaming Works · Use Cases For P2p Streaming · The Future Of P2p Streaming
[80]
Open Source Licenses In 2022: Trends And Predictions - Mend.io
Jan 27, 2022 · The Apache 2.0 license and the MIT License are far more popular than the GPL family, together comprising over 50% of the top open source licenses currently in ...Open Source Licenses Trends... · The Mit Open Source License... · The Gnu Gpl Family Continues...
[81]
Protecting the Software Supply Chain: Cautionary Tales and Trends
Aug 10, 2022 · We've seen warnings for the past decade about the risk of stolen code signing keys to digitally sign and distribute malware as “trusted.
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Code Signing, Mitigation M1045 - Enterprise | MITRE ATT&CK®
Jun 11, 2019 · Code signing is a security process that ensures the authenticity and integrity of software by digitally signing executables, scripts, and other code artifacts.
[83]
How Code Signing Helps in the Software Development Cycle
May 4, 2025 · Code signing is crucial in securing the software supply chain against tampering, malware, and unauthorized modifications. Real-world attacks ...
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[PDF] Covariate Shift Adaptation by Importance Weighted Cross Validation
Model selection is one of the key ingredients in machine learning. However, under the covariate shift, a standard model selection technique such as cross ...
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[PDF] Visual Domain Adaptation: A Survey of Recent Advances
Although some special kinds of domain adaptation problems have been studied under different names such as covariate shift [1], class imbalance [4], and sample ...
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SKADA-Bench: Benchmarking Unsupervised Domain Adaptation ...
Oct 7, 2025 · Unsupervised Domain Adaptation (DA) consists of adapting a model trained on a labeled source domain to perform well on an unlabeled target ...
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[PDF] Improving robustness against common corruptions by covariate shift ...
We demonstrate that this simple adaptation alone can greatly increase recognition performance on corrupted images. Our contributions can be summarized as ...<|separator|>
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[PDF] Markov chain Monte Carlo 1 Introduction - probability.ca
MCMC algorithms are all constructed to have π as a stationary distribution. However, we require extra conditions to ensure that they converge in distribution to ...
[89]
Markov Chain Monte Carlo Convergence - Pumas Tutorials
MCMC asymptotically convergence stems from the Central Limit Theorem (CLT) for Makov Chains. The assumption is that the parameters have finite variance.
[90]
[PDF] Convergence diagnostics for Markov chain Monte Carlo - arXiv
Oct 16, 2019 · The main idea behind this method, known as burn-in, is to use samples only after the Markov chain gets sufficiently close to the stationary ...
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[PDF] Power laws, Pareto distributions and Zipf's law - Projects at Harvard
When the probability of measuring a particular value of some quantity varies inversely as a power of that value, the quantity is said to follow a power law, ...
[92]
[PDF] Power laws and preferential attachment - SNAP: Stanford
Zipf's law & AOL site visits. □Deviation from Zipf's law. □ slightly too few websites with large numbers of visitors: Page 77. Zipf's Law and city sizes (~1930) ...
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Write Skew and Zipf Distribution: Evidence and Implications
Jun 8, 2016 · We demonstrate that the Zipf-like pattern indeed widely exists in write traffic provided its disguises are removed by statistical processing.
[94]
What Is Physical Distribution in Supply Chain Management?
May 8, 2025 · The channels involved include warehousing, inventory control, order processing, materials handling, transportation, and customer service.
[95]
Understanding Supply Chain Management (SCM) and Its Importance
Discover how supply chain management optimizes production and distribution, reduces costs, and enhances efficiency from raw materials to customer delivery.
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Economic Order Quantity (EOQ) Defined - NetSuite
May 10, 2021 · Economic order quantity (EOQ) is a calculation representing the ideal order size to meet demand without overspending, minimizing costs.What Does Economic Order... · Challenges of Economic Order... · EOQ Examples
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Just-in-Time (JIT): Definition, Example, Pros, and Cons - Investopedia
The just-in-time (JIT) inventory system minimizes inventory and increases efficiency. JIT production systems cut inventory costs because manufacturers receive ...
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Just-in-Time (JIT) Inventory: A Definition and Comprehensive Guide
Nov 8, 2024 · Benefits of JIT Inventory Management. JIT inventory management boosts a company's ROI by lowering inventory carrying costs, increasing ...Pros and cons of JIT inventory... · Questions to help determine...
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Understanding the WTO - The case for open trade - WTO
Simply put, the principle of “comparative advantage” says that countries prosper first by taking advantage of their assets in order to concentrate on what they ...
[100]
International (Global) Trade: Definition, Benefits, and Criticisms
Global trade allows wealthy countries to use their resources more efficiently. This also allows some countries to produce the same good more efficiently; in ...<|separator|>
[101]
How Trade Agreements Have Enhanced the Freedom and ...
Aug 27, 2024 · The service sector enjoyed most of the economic gains from trade agreements, but the manufacturing sector also grew by $3.5 billion compared to ...
[102]
Trump Tariffs: Tracking the Economic Impact of the Trump Trade War
The first Trump administration-imposed tariffs on thousands of products valued at approximately $380 billion in 2018 and 2019, affecting approximately 15 ...
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https://www.aeaweb.org/articles?id=10.1257/jep.33.4.187
[104]
[PDF] The Economic Impacts of the US-China Trade War
Relatedly, if supply chains involve two-way trade within narrow product categories, then US import tariffs may raise costs along the chain, also increasing ...
[105]
Balancing Cost and Resilience: The New Supply Chain Challenge
Jul 18, 2025 · We call this new operating model the “cost of resilience” mindset. It’s about striking the right balance between cost competitiveness and agility.
[106]
How the 2018/19 US tariffs against China boosted exports ... - CEPR
Jun 21, 2025 · We estimate that a 25 percentage point increase in US tariffs on Chinese goods raised Mexican exports to the US by 4.2%. This increase occurred ...
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McKinsey Global Supply Chain Leader Survey 2024
Oct 14, 2024 · We surveyed 88 global supply chain leaders across seven industries about their networks, planning, digitization, and risk management.
[108]
Nearshoring to Mexico and US Supply Chain Resilience as a ...
Dec 22, 2023 · Our findings show that both China and Mexico were able to quickly recover from the disruption of their supply chains by the COVID-19 pandemic.
[109]
Supply chain resilience | Deloitte Insights
May 23, 2024 · Government incentives and investment opportunities for advanced technology supply chains. The US government is incentivizing businesses across ...
[110]
AI in Demand Planning: Transforming Strategies for Supply Chain ...
Jul 9, 2025 · By embracing AI-driven demand forecasting, manufacturers can better understand historical patterns, detect emerging trends, and rapidly respond ...
[111]
Why AI Predictive Analytics is Essential for Supply Chain Success
Mar 31, 2025 · It will grow from $17.07 billion in 2024 to $20.77 billion in 2025 at a compound annual growth rate (CAGR) of 21.6%. The predictive analytics ...
[112]
Future of Inventory Management: How AI Forecasting is ... - SuperAGI
Jun 29, 2025 · AI forecasting in 2025 offers unprecedented accuracy, efficiency, and automation, reducing errors by 20-50%, and up to 85% improvement in ...Why Ai Forecasting Matters · Predictive Analytics For... · Autonomous Inventory...
[113]
Autonomous Mobile Robots Statistics and Facts (2025)
By 2026, 70% of mobile robots in logistics and manufacturing are projected to utilize IoT technology for enhanced performance. Conclusion. Autonomous Mobile ...
[114]
Top Warehouse Trends for 2025: Future of Automation - Exotec
Apr 15, 2025 · Top trends include robotic automation, sustainability, AI, cybersecurity, and flexible, modular systems for a dynamic, tech-driven warehouse.
[115]
A literature review on green supply chain management for ...
GSCM offers numerous benefits, viz. it (i) minimizes waste, (ii) lowers carbon footprints, and (iii) enhances resource efficiency and environmental performance, ...
[116]
The fallacy of profitable green supply chains - ScienceDirect.com
The results suggest that pursuing GSCM can bring trade-offs into play, demonstrating a paradoxical view of enhanced sustainability versus less profitability.Missing: critiques | Show results with:critiques<|control11|><|separator|>
[117]
Supply Chain Sustainability: What, Why, and Best Practices - Gartner
Sustainability is helping executives optimize and reduce costs. For many organizations, energy costs are significant, and 80% of business leaders we surveyed ...