Journal articles: 'Power law distribution'

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Newman, Mark. "Power-law distribution." Significance 14, no. 4 (August 2017): 10–11. http://dx.doi.org/10.1111/j.1740-9713.2017.01050.x.

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CHEN, YANGUANG. "POWER-LAW DISTRIBUTIONS BASED ON EXPONENTIAL DISTRIBUTIONS: LATENT SCALING, SPURIOUS ZIPF'S LAW, AND FRACTAL RABBITS." Fractals 23, no. 02 (May 28, 2015): 1550009. http://dx.doi.org/10.1142/s0218348x15500097.

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The difference between the inverse power function and the negative exponential function is significant. The former suggests a complex distribution, while the latter indicates a simple distribution. However, the association of the power-law distribution with the exponential distribution has been seldom researched. This paper is devoted to exploring the relationships between exponential laws and power laws from the angle of view of urban geography. Using mathematical derivation and numerical experiments, I reveal that a power-law distribution can be created through a semi-moving average process of an exponential distribution. For the distributions defined in a one-dimension space (e.g. Zipf's law), the power exponent is 1; while for those defined in a two-dimension space (e.g. Clark's law), the power exponent is 2. The findings of this study are as follows. First, the exponential distributions suggest a hidden scaling, but the scaling exponents suggest a Euclidean dimension. Second, special power-law distributions can be derived from exponential distributions, but they differ from the typical power-law distributions. Third, it is the real power-law distributions that can be related with fractal dimension. This study discloses an inherent link between simplicity and complexity. In practice, maybe the result presented in this paper can be employed to distinguish the real power laws from spurious power laws (e.g. the fake Zipf distribution).

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TAKAYASU, HIDEKI. "POWER-LAW DISTRIBUTION OF RIVER BASIN SIZES." Fractals 01, no. 03 (September 1993): 521–28. http://dx.doi.org/10.1142/s0218348x9300054x.

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River models are reviewed with emphasis on the power-law nature of basin size distributions. From a general point of view, the whole river pattern on a surface can be regarded as a kind of tiling by random self-affine branches. Applying the idea of stable distributions, we show that the self-affinity and tiling condition naturally derive the power-law basin size distribution.

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Campolieti, Michele. "Power Law Distributions and the Size Distribution of Strikes." Sociological Methods & Research 48, no. 3 (October 10, 2017): 561–87. http://dx.doi.org/10.1177/0049124117729709.

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Using Canadian data from 1976 to 2014, I study the size distribution of strikes with three alternative measures of strike size: the number of workers on strike, strike duration in calendar days, and the number of person calendar days lost to a strike. I use a maximum likelihood framework that provides a way to estimate distributions, evaluate model fit, and also test against alternative distributions. I consider a few theories that can create power law distributions in strike size, such as the joint costs model that posits strike size is inversely proportional to dispute costs. I find that the power law distribution fits the data for the number of lost person calendar days relatively well and is also more appropriate than the lognormal distribution. I also discuss the implications of my findings from a methodological, research, and policy perspective.

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Guo, Ran, and Jiulin Du. "Are power-law distributions an equilibrium distribution or a stationary nonequilibrium distribution?" Physica A: Statistical Mechanics and its Applications 406 (July 2014): 281–86. http://dx.doi.org/10.1016/j.physa.2014.03.056.

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BURROUGHS, STEPHEN M., and SARAH F. TEBBENS. "UPPER-TRUNCATED POWER LAW DISTRIBUTIONS." Fractals 09, no. 02 (June 2001): 209–22. http://dx.doi.org/10.1142/s0218348x01000658.

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Power law cumulative number-size distributions are widely used to describe the scaling properties of data sets and to establish scale invariance. We derive the relationships between the scaling exponents of non-cumulative and cumulative number-size distributions for linearly binned and logarithmically binned data. Cumulative number-size distributions for data sets of many natural phenomena exhibit a "fall-off" from a power law at the largest object sizes. Previous work has often either ignored the fall-off region or described this region with a different function. We demonstrate that when a data set is abruptly truncated at large object size, fall-off from a power law is expected for the cumulative distribution. Functions to describe this fall-off are derived for both linearly and logarithmically binned data. These functions lead to a generalized function, the upper-truncated power law, that is independent of binning method. Fitting the upper-truncated power law to a cumulative number-size distribution determines the parameters of the power law, thus providing the scaling exponent of the data. Unlike previous approaches that employ alternate functions to describe the fall-off region, an upper-truncated power law describes the data set, including the fall-off, with a single function.

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Song, W. G., H. P. Zhang, T. Chen, and W. C. Fan. "Power-law distribution of city fires." Fire Safety Journal 38, no. 5 (September 2003): 453–65. http://dx.doi.org/10.1016/s0379-7112(02)00084-x.

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Zhu, Jianlin, and Zhiguo Liu. "Power-law distribution of acid deposition." International Journal of Environment and Pollution 19, no. 1 (2003): 11. http://dx.doi.org/10.1504/ijep.2003.002345.

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GUPTA, HARI M., JOSÉ R. CAMPANHA, and FERNANDO D. PRADO. "POWER LAW DISTRIBUTION IN EDUCATION: UNIVERSITY ENTRANCE EXAMINATION." International Journal of Modern Physics C 11, no. 06 (September 2000): 1273–79. http://dx.doi.org/10.1142/s0129183100001085.

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We studied the statistical distribution of candidate's performance which is measured through their marks in university entrance examination (Vestibular) of UNESP (Universidade Estadual Paulista) for years 1998, 1999, and 2000. All students are divided in three groups: Physical, Biological and Humanities. We paid special attention to the examination of Portuguese language which is common for all and examinations for the particular area. We observed long ubiquitous power law tails in Physical and Biological sciences. This indicate the presence of strong positive feedback in sciences. We are able to explain completely these statistical distributions through Gradually Truncated Power law distributions which we developed recently to explain statistical behavior of financial market. The statistical distribution in case of Portuguese language and humanities is close to normal distribution. We discuss the possible reason for this peculiar behavior.

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Minasandra, Pranav, and Kavita Isvaran. "Truncated power-law distribution of group sizes in antelope." Behaviour 157, no. 6 (June 11, 2020): 541–58. http://dx.doi.org/10.1163/1568539x-bja10012.

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Abstract Quantifying and understanding group size distributions can be useful for understanding group behaviour in animal populations. We analysed group size data of the blackbuck, Antilope cervicapra, from six different field sites to estimate the group size distribution of this antelope. We used likelihood based methods (AICs and likelihood ratios) to show that an exponentially truncated power law is the distribution that best describes blackbuck group data, outperforming a simple power-law, an exponential distribution, and a lognormal distribution. Our results show that distribution parameters can be used to draw novel insights regarding group dynamics, and we demonstrate this by investigating how habitat openness affects group size distributions.

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Baes, Maarten, and Peter Camps. "The dynamical structure of broken power-law and double power-law models for dark matter haloes." Monthly Notices of the Royal Astronomical Society 503, no. 2 (March 4, 2021): 2955–65. http://dx.doi.org/10.1093/mnras/stab634.

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ABSTRACT Galaxy kinematics and gravitational lensing are two complementary ways to constrain the distribution of dark matter on galaxy scales. The typical dark matter density profiles adopted in dynamical studies cannot easily be adopted in lensing studies. Ideally, a mass model should be used that has the global characteristics of realistic dark matter distributions, and that allows for an analytical calculation of the magnifications and deflection angles. A simple model with these properties, the broken power-law (BPL) model, has very recently been introduced. We examine the dynamical structure of the family of BPL models. We derive simple closed expressions for basic dynamical properties, and study the distribution function under the assumption of velocity isotropy. We find that none of the BPL models with realistic parameters has an isotropic distribution function that is positive over the entire phase space, implying that the BPL models cannot be supported by an isotropic velocity distribution, or models with a more radially anisotropic orbital structure. This result limits the attractiveness of the BPL family as a tool for lensing studies to some degree. More generally, we find that not all members of the general family of double power-law or Zhao models, often used to model dark matter haloes, can be supported by an isotropic or radially anisotropic distribution function. In other words, the distribution function may become negative even for spherically symmetric models with a well-behaved density profile.

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Jin, Zhaoyan, and Quanyuan Wu. "Using Power-Law Degree Distribution to Accelerate PageRank." Computer Engineering and Applications Journal 1, no. 2 (December 15, 2012): 63–70. http://dx.doi.org/10.18495/comengapp.v1i2.8.

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The PageRank vector of a network is very important, for it can reflect the importance of a Web page in the World Wide Web, or of a people in a social network. However, with the growth of the World Wide Web and social networks, it needs more and more time to compute the PageRank vector of a network. In many real-world applications, the degree and PageRank distributions of these complex networks conform to the Power-Law distribution. This paper utilizes the degree distribution of a network to initialize its PageRank vector, and presents a Power-Law degree distribution accelerating algorithm of PageRank computation. Experiments on four real-world datasets show that the proposed algorithm converges more quickly than the original PageRank algorithm.DOI:Â 10.18495/comengapp.12.063070

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Artico, I., I. Smolyarenko, V. Vinciotti, and E. C. Wit. "How rare are power-law networks really?" Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2241 (September 2020): 20190742. http://dx.doi.org/10.1098/rspa.2019.0742.

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The putative scale-free nature of real-world networks has generated a lot of interest in the past 20 years: if networks from many different fields share a common structure, then perhaps this suggests some underlying ‘network law’. Testing the degree distribution of networks for power-law tails has been a topic of considerable discussion. Ad hoc statistical methodology has been used both to discredit power-laws as well as to support them. This paper proposes a statistical testing procedure that considers the complex issues in testing degree distributions in networks that result from observing a finite network, having dependent degree sequences and suffering from insufficient power. We focus on testing whether the tail of the empirical degrees behaves like the tail of a de Solla Price model, a two-parameter power-law distribution. We modify the well-known Kolmogorov–Smirnov test to achieve even sensitivity along the tail, considering the dependence between the empirical degrees under the null distribution, while guaranteeing sufficient power of the test. We apply the method to many empirical degree distributions. Our results show that power-law network degree distributions are not rare, classifying almost 65% of the tested networks as having a power-law tail with at least 80% power.

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Kagan, Yan Y. "Earthquake size distribution: Power-law with exponent ?" Tectonophysics 490, no. 1-2 (July 2010): 103–14. http://dx.doi.org/10.1016/j.tecto.2010.04.034.

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Takayasu, H., A. Provata, and M. Takayasu. "Stability and relaxation of power-law distribution." Physical Review A 42, no. 12 (December 1, 1990): 7087–90. http://dx.doi.org/10.1103/physreva.42.7087.

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Dresner, Lawrence. "Current distribution in multilayer power-law cryoconductors." Cryogenics 38, no. 2 (February 1998): 205–9. http://dx.doi.org/10.1016/s0011-2275(97)00096-9.

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Ichinomiya, Takashi. "Power-law distribution in Japanese racetrack betting." Physica A: Statistical Mechanics and its Applications 368, no. 1 (August 2006): 207–13. http://dx.doi.org/10.1016/j.physa.2005.12.027.

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Nacher, J. C., and T. Ochiai. "Power-law distribution of gene expression fluctuations." Physics Letters A 372, no. 40 (September 2008): 6202–6. http://dx.doi.org/10.1016/j.physleta.2008.08.023.

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Melkumyan, A. A., A. V. Belov, M. A. Abunina, A. A. Abunin, E. A. Eroshenko, V. G. Yanke, and V. A. Oleneva. "Power Law Distribution of Forbush Decrease Magnitude." Research Notes of the AAS 2, no. 2 (June 11, 2018): 49. http://dx.doi.org/10.3847/2515-5172/aaca95.

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Collier, Andrew B., Thomas Gjesteland, and Nikolai Østgaard. "Assessing the power law distribution of TGFs." Journal of Geophysical Research: Space Physics 116, A10 (October 2011): n/a. http://dx.doi.org/10.1029/2011ja016612.

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Şimşek, Emrah, and Minsu Kim. "Power-law tail in lag time distribution underlies bacterial persistence." Proceedings of the National Academy of Sciences 116, no. 36 (August 19, 2019): 17635–40. http://dx.doi.org/10.1073/pnas.1903836116.

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Genetically identical microbial cells respond to stress heterogeneously, and this phenotypic heterogeneity contributes to population survival. Quantitative analysis of phenotypic heterogeneity can reveal dynamic features of stochastic mechanisms that generate heterogeneity. Additionally, it can enable a priori prediction of population dynamics, elucidating microbial survival strategies. Here, we quantitatively analyzed the persistence of an Escherichia coli population. When a population is confronted with antibiotics, a majority of cells is killed but a subpopulation called persisters survives the treatment. Previous studies have found that persisters survive antibiotic treatment by maintaining a long period of lag phase. When we quantified the lag time distribution of E. coli cells in a large dynamic range, we found that normal cells rejuvenated with a lag time distribution that is well captured by an exponential decay [exp(−kt)], agreeing with previous studies. This exponential decay indicates that their rejuvenation is governed by a single rate constant kinetics (i.e., k is constant). Interestingly, the lag time distribution of persisters exhibited a long tail captured by a power-law decay. Using a simple quantitative argument, we demonstrated that this power-law decay can be explained by a wide variation of the rate constant k. Additionally, by developing a mathematical model based on this biphasic lag time distribution, we quantitatively explained the complex population dynamics of persistence without any ad hoc parameters. The quantitative features of persistence demonstrated in our work shed insights into molecular mechanisms of persistence and advance our knowledge of how a microbial population evades antibiotic treatment.

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Lee, Kang-won, and Ji-sang Lee. "Power-Law of Node Degree Distribution and Information Diffusion Process." Journal of Korean Institute of Communications and Information Sciences 44, no. 10 (October 31, 2019): 1866–77. http://dx.doi.org/10.7840/kics.2019.44.10.1866.

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SHIN, J. K., and G. S. SHIN. "DEVIATION OF THE POWER-LAW BY GEOMETRIC AGING EFFECT." Fractals 15, no. 02 (June 2007): 139–49. http://dx.doi.org/10.1142/s0218348x07003514.

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An agent-based model is employed for the study of the group size distributions. A fixed number of homogeneous agents are distributed on a two-dimensional lattice system. The dynamics of the agents is described in terms of the inverse distance potential and the friction factor. From a random initial distribution, the agents move forming groups until all the agents come to a stationary position. For a squared system with L × L cells, the group size distribution showed a well defined power-law behavior up to the cut-off size. But when the system changed to an L × H non-squared one, a "geometric aging effect" emerged. Together with the phase transition, the geometric aging effect is considered to be a generic mechanism of the deviated power-law distributions, such as the "fall-off" and the three-bent-line distributions. The results are discussed in relation to the well-known physical or social phenomena such as the King Effect in the city size distributions, the fall-off distribution of the fish schools, the three-bent-line distributions of the Earth-crossing asteroids and 2D percolation problem.

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Levy, Moshe. "Gibrat's Law for (All) Cities: Comment." American Economic Review 99, no. 4 (August 1, 2009): 1672–75. http://dx.doi.org/10.1257/aer.99.4.1672.

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Jan Eeckhout (2004) reports that the empirical city size distribution is lognormal, consistent with Gibrat's Law. We show that for the top 0.6 percent of the largest cities, the empirical distribution is dramatically different from the lognormal, and follows a power law. This top part is extremely important as it accounts for more than 23 percent of the population. The empirical hybrid lognormal-power-law distribution revealed may be characteristic of other key distributions, such as the wealth distribution and the income distribution. This distribution is not consistent with a simple Gibrat proportionate effect process, and its origin presents a puzzle yet to be answered. (JEL R11, R12, R23)

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Corral, Álvaro, and Isabel Serra. "The Brevity Law as a Scaling Law, and a Possible Origin of Zipf’s Law for Word Frequencies." Entropy 22, no. 2 (February 17, 2020): 224. http://dx.doi.org/10.3390/e22020224.

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An important body of quantitative linguistics is constituted by a series of statistical laws about language usage. Despite the importance of these linguistic laws, some of them are poorly formulated, and, more importantly, there is no unified framework that encompasses all them. This paper presents a new perspective to establish a connection between different statistical linguistic laws. Characterizing each word type by two random variables—length (in number of characters) and absolute frequency—we show that the corresponding bivariate joint probability distribution shows a rich and precise phenomenology, with the type-length and the type-frequency distributions as its two marginals, and the conditional distribution of frequency at fixed length providing a clear formulation for the brevity-frequency phenomenon. The type-length distribution turns out to be well fitted by a gamma distribution (much better than with the previously proposed lognormal), and the conditional frequency distributions at fixed length display power-law-decay behavior with a fixed exponent α ≃ 1.4 and a characteristic-frequency crossover that scales as an inverse power δ ≃ 2.8 of length, which implies the fulfillment of a scaling law analogous to those found in the thermodynamics of critical phenomena. As a by-product, we find a possible model-free explanation for the origin of Zipf’s law, which should arise as a mixture of conditional frequency distributions governed by the crossover length-dependent frequency.

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KANIADAKIS, G. "PHYSICAL ORIGIN OF THE POWER-LAW TAILED STATISTICAL DISTRIBUTIONS." Modern Physics Letters B 26, no. 10 (April 8, 2012): 1250061. http://dx.doi.org/10.1142/s0217984912500613.

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Starting from the BBGKY hierarchy, describing the kinetics of nonlinear particle system, we obtain the relevant entropy and stationary distribution function. Subsequently, by employing the Lorentz transformations we propose the relativistic generalization of the exponential and logarithmic functions. The related particle distribution and entropy represents the relativistic extension of the classical Maxwell–Boltzmann distribution and of the Boltzmann entropy, respectively, and define the statistical mechanics presented in [Phys. Rev. E66 (2002) 056125] and [Phys. Rev. E72 (2005) 036108]. The achievements of the present effort, support the idea that the experimentally observed power-law tailed statistical distributions in plasma physics, are enforced by the relativistic microscopic particle dynamics.

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Reynolds, A. M. "Exponential and Power-Law Contact Distributions Represent Different Atmospheric Conditions." Phytopathology® 101, no. 12 (December 2011): 1465–70. http://dx.doi.org/10.1094/phyto-01-11-0001.

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It is well known that the dynamics of plant disease epidemics are very sensitive to the functional form of the contact distribution—the probability distribution function for the distance of viable fungal spore movement until deposition. Epidemics can take the form of a constant-velocity travelling wave when the contact distribution is exponentially bounded. Fat-tailed contact distributions, on the other hand, lead to epidemic spreads that accelerate over time. Some empirical data for contact distributions can be well represented by negative exponentials while other data are better represented by fat-tailed inverse power laws. Here we present data from numerical simulations that suggest that negative exponentials and inverse power laws are not competing candidate forms of the contact distribution but are instead representative of different atmospheric conditions. Contact distributions for atmospheric boundary-layers with stabilities ranging from strongly convective (a hot windless day time scenario) to stable stratification (a cold windy night time scenario) but without precipitation events are calculated using well-established state-of-the-art Lagrangian stochastic (particle tracking) dispersal models. Contact distributions are found to be well represented by exponentials for strongly convective conditions; a –3/2 inverse power law for convective boundary-layers with wind shear; and by a –2/3 inverse power law for stably stratified conditions.

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WICHMANN, SØREN. "On the power-law distribution of language family sizes." Journal of Linguistics 41, no. 1 (March 2005): 117–31. http://dx.doi.org/10.1017/s002222670400307x.

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When the sizes of language families of the world, measured by the number of languages contained in each family, are plotted in descending order on a diagram where the x-axis represents the place of each family in the rank-order (the largest family having rank 1, the next-largest, rank 2, and so on) and the y-axis represents the number of languages in the family determining the rank-ordering, it is seen that the distribution closely approximates a curve defined by the formula y=ax−b. Such ‘power-law’ distributions are known to characterize a wide range of social, biological, and physical phenomena and are essentially of a stochastic nature. It is suggested that the apparent power-law distribution of language family sizes is of relevance when evaluating overall classifications of the world's languages, for the analysis of taxonomic structures, for developing hypotheses concerning the prehistory of the world's languages, and for modelling the future extinction of language families.

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Bates, David, and Adam Wright. "Distribution of Problems, Medications and Lab Results in Electronic Health Records: The Pareto Principle at Work." Applied Clinical Informatics 01, no. 01 (2010): 32–37. http://dx.doi.org/10.4338/aci-2009-12-ra-0023.

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SummaryBackground: Many natural phenomena demonstrate power-law distributions, where very common items predominate. Problems, medications and lab results represent some of the most important data elements in medicine, but their overall distribution has not been reported.Objective: Our objective is to determine whether problems, medications and lab results demonstrate a power law distribution.Methods: Retrospective review of electronic medical record data for 100,000 randomly selected patients seen at least twice in 2006 and 2007 at the Brigham and Women’s Hospital in Boston and its affiliated medical practices.Results: All three data types exhibited a power law distribution. The 12.5% most frequently used problems account for 80% of all patient problems, the top 11.8% of medications account for 80% of all medication orders and the top 4.5% of lab result types account for all lab results.Conclusion: These three data elements exhibited power law distributions with a small number of common items representing a substantial proportion of all orders and observations, which has implications for electronic health record design.

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Burkert, A., M. R. Bate, and P. Bodenheimer. "Protostellar fragmentation in a power-law density distribution." Monthly Notices of the Royal Astronomical Society 289, no. 3 (August 11, 1997): 497–504. http://dx.doi.org/10.1093/mnras/289.3.497.

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Balthrop, Andrew, and Siyu Quan. "The power-law distribution of cumulative coal production." Physica A: Statistical Mechanics and its Applications 530 (September 2019): 121573. http://dx.doi.org/10.1016/j.physa.2019.121573.

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Tang, Lei-H., J. Kertesz, and D. E. Wolf. "Kinetic roughening with power-law waiting time distribution." Journal of Physics A: Mathematical and General 24, no. 19 (October 7, 1991): L1193—L1200. http://dx.doi.org/10.1088/0305-4470/24/19/011.

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Ning, Ding, and Wang You-Gui. "Power-Law Tail in the Chinese Wealth Distribution." Chinese Physics Letters 24, no. 8 (July 26, 2007): 2434–36. http://dx.doi.org/10.1088/0256-307x/24/8/076.

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TAYLOR, R. A. J. "Spatial distribution, sampling efficiency and Taylor's power law." Ecological Entomology 43, no. 2 (November 13, 2017): 215–25. http://dx.doi.org/10.1111/een.12487.

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Gabriel, S. B., and J. Feynman. "Power-law distribution for solar energetic proton events." Solar Physics 165, no. 2 (May 1996): 337–46. http://dx.doi.org/10.1007/bf00149718.

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赖, 世刚. "Power Law Distribution of Urban Population in China." Urbanization and Land Use 02, no. 01 (2014): 1–7. http://dx.doi.org/10.12677/ulu.2014.21001.

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de Vries, H., T. Becker, and B. Eckhardt. "Power law distribution of discharge in ideal networks." Water Resources Research 30, no. 12 (December 1994): 3541–43. http://dx.doi.org/10.1029/94wr02178.

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Park, K., and E. Domany. "Power law distribution of dividends in horse races." Europhysics Letters (EPL) 53, no. 4 (February 2001): 419–25. http://dx.doi.org/10.1209/epl/i2001-00169-0.

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Rios, P. De Los. "Power law size distribution of supercritical random trees." Europhysics Letters (EPL) 56, no. 6 (December 2001): 898–903. http://dx.doi.org/10.1209/epl/i2001-00604-2.

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Goldstein, M. L., S. A. Morris, and G. G. Yen. "Problems with fitting to the power-law distribution." European Physical Journal B 41, no. 2 (September 2004): 255–58. http://dx.doi.org/10.1140/epjb/e2004-00316-5.

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Lombardi, Marco, João Alves, and Charles J. Lada. "Molecular clouds have power-law probability distribution functions." Astronomy & Astrophysics 576 (March 13, 2015): L1. http://dx.doi.org/10.1051/0004-6361/201525650.

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Adamic, Lada A., Bernardo A. Huberman, A. L. Barabási, R. Albert, H. Jeong, and G. Bianconi. "Power-Law Distribution of the World Wide Web." Science 287, no. 5461 (March 24, 2000): 2115. http://dx.doi.org/10.1126/science.287.5461.2115a.

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Akhundjanov, Sherzod B., and Lauren Chamberlain. "The power-law distribution of agricultural land size." Journal of Applied Statistics 46, no. 16 (June 5, 2019): 3044–56. http://dx.doi.org/10.1080/02664763.2019.1624695.

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Fix, Blair. "Hierarchy and the power-law income distribution tail." Journal of Computational Social Science 1, no. 2 (July 16, 2018): 471–91. http://dx.doi.org/10.1007/s42001-018-0019-8.

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Mahnke, Reinhard, Jevgenijs Kaupužs, and Mārtiņš Brics. "Power Laws and Skew Distributions." Communications in Computational Physics 12, no. 3 (September 2012): 721–31. http://dx.doi.org/10.4208/cicp.010411.050811a.

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AbstractPower-law distributions and other skew distributions, observed in various models and real systems, are considered. A model, describing evolving systems with increasing number of elements, is considered to study the distribution over element sizes. Stationary power-law distributions are found. Certain non-stationary skew distributions are obtained and analyzed, based on exact solutions and numerical simulations.

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Lemoine, Martin, and Mikhail A. Malkov. "Power-law spectra from stochastic acceleration." Monthly Notices of the Royal Astronomical Society 499, no. 4 (October 13, 2020): 4972–83. http://dx.doi.org/10.1093/mnras/staa3131.

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ABSTRACT Numerical simulations of particle acceleration in magnetized turbulence have recently observed power-law spectra where pile-up distributions are rather expected. We interpret this as evidence for particle segregation based on acceleration rate, which is likely related to a non-trivial dependence of the efficacy of acceleration on phase space variables other than the momentum. We describe the corresponding transport in momentum space using continuous-time random walks, in which the time between two consecutive momentum jumps becomes a random variable. We show that power laws indeed emerge when the experimental (simulation) time-scale does not encompass the full extent of the distribution of waiting times. We provide analytical solutions, which reproduce dedicated numerical Monte Carlo realizations of the stochastic process, as well as analytical approximations. Our results can be readily extrapolated for applications to astrophysical phenomenology.

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DELLI GATTI, DOMENICO, CORRADO DI GUILMI, EDOARDO GAFFEO, GIANFRANCO GIULIONI, MAURO GALLEGATI, and ANTONIO PALESTRINI. "BUSINESS CYCLE FLUCTUATIONS AND FIRMS' SIZE DISTRIBUTION DYNAMICS." Advances in Complex Systems 07, no. 02 (June 2004): 223–40. http://dx.doi.org/10.1142/s0219525904000160.

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Power law behavior is an emerging property of many economic models. In this paper we emphasize the fact that power law distributions are persistent but not time invariant. In fact, the scale and shape of the firms' size distribution fluctuate over time. In particular, on a log–log space, both the intercept and the slope of the power law distribution of firms' size change over the cycle: during expansions (recessions) the straight line representing the distribution shifts up and becomes less steep (steeper). We show that the empirical distributions generated by simulations of the model presented in Ref. 11 mimic real empirical distributions remarkably well.

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Hantson, Stijn, Salvador Pueyo, and Emilio Chuvieco. "Global fire size distribution: from power law to log-normal." International Journal of Wildland Fire 25, no. 4 (2016): 403. http://dx.doi.org/10.1071/wf15108.

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Wildland fires are one of the main alleged examples of Self-Organised Criticality (SOC), with simple SOC models resulting in the expectation of a power-law fire size frequency distribution. Here, we test whether fire size distributions systematically follow a power law and analyse their spatial variation for eight distinct areas over the globe. For each of the areas, we examine the fire size frequency distribution using two types of plots, maximum likelihood estimation and chi-square tests. Log-normal emerges as a suitable option to fit the fire size distribution in this variety of environments. In only two of eight areas was the power law (which is a particular case of the log-normal) not rejected. Notably, the two parameters of log-normal are related to each other, displaying a general linear relation, which extends to the sites that can be described with a power law. These results do not necessarily refute the SOC hypothesis, but reveal the presence of other processes that are, at least, modulating the outcome of SOC in some areas.

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Jodra, Pedro, Hector Wladimir Gomez, Maria Dolores Jimenez-Gamero, and Maria Virtudes Alba-Fernandez. "THE POWER MUTH DISTRIBUTION∗." Mathematical Modelling and Analysis 22, no. 2 (March 18, 2017): 186–201. http://dx.doi.org/10.3846/13926292.2017.1289481.

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Muth introduced a probability distribution with application in reliability theory. We propose a new model from the Muth law. This paper studies its statistical properties, such as the computation of the moments, computer generation of pseudo-random data and the behavior of the failure rate function, among others. The estimation of parameters is carried out by the method of maximum likelihood and a Monte Carlo simulation study assesses the performance of this method. The practical usefulness of the new model is illustrated by means of two real data sets, showing that it may provide a better fit than other probability distributions.

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OWEN, W. J., and W. J. PADGETT. "POWER-LAW ACCELERATED BIRNBAUM–SAUNDERS LIFE MODELS." International Journal of Reliability, Quality and Safety Engineering 07, no. 01 (March 2000): 1–15. http://dx.doi.org/10.1142/s021853930000002x.

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An accelerated life testing procedure can reduce the lifetime of a material by observing the material's behavior under higher levels of stress than what is normally encountered. Useful inference hinges on the selection of an appropriate lifetime distribution and the substitution of an acceleration model for a distribution parameter, such as the mean or scale. The (inverse) power-law model is one such acceleration model that has applications to fatigue studies in metals, where failure tends to be crack-induced. The Birnbaum–Saunders distribution was developed to model fatigue in materials where the failure of a specimen is due to the propagation of a dominant crack. This paper will compare two Birnbaum–Saunders type models from the literature (that have power-law accelerated features) with a new but distinctive model proposed here. The new model is an accelerated life model for a reparameterization of the baseline distribution. Comparison of the three models will be via the aluminum coupon data set from Birnbaum and Saunders5 and issues of accelerated testing will be discussed.

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Journal articles on the topic 'Power law distribution'

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