On a Class of Skew Distribution Functions

Simon, Herbert A.

doi:10.1093/biomet/42.3-4.425

Cited by 1,852 publications

(893 citation statements)

References 10 publications

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“…Importantly, the rule depends on the existing population. Thus the observed population cannot be considered to be a simple sampling from a given distribution [626]. Rather, the distribution characterizing the population changes as a result of applying the rule and generating additional members.…”

Section: Generative Modelsmentioning

confidence: 99%

“…Yule's work was later extended and updated by Simon [626]. Simon showed that essentially the same model may be applied to diverse situations, including linguistics (explaining the origin of Zipf's law), geography (the distribution of city sizes), and economics (harking back to Pareto's work on the distribution of wealth).…”

Section: Preferential Attachmentmentioning

confidence: 99%

“…The following table shows Simon's mapping of this model to different contexts [626]. Note that in the latter two or three examples it makes sense to only consider elements larger than a certain threshold.…”

Section: Preferential Attachmentmentioning

confidence: 99%

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Workload Modeling for Computer Systems Performance Evaluation

Feitelson

2015

191

131

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Reliable performance evaluations require the use of representative workloads. This is no easy task since modern computer systems and their workloads are complex, with many interrelated attributes and complicated structures. Experts often use sophisticated mathematics to analyze and describe workload models, making these models difficult for practitioners to grasp. This book aims to close this gap by emphasizing the intuition and the reasoning behind the definitions and derivations related to the workload models. It provides numerous examples from real production systems, with hundreds of graphs. Using this book, readers will be able to analyze collected workload data and clean it if necessary, derive statistical models that include skewed marginal distributions and correlations, and consider the need for generative models and feedback from the system. The descriptive statistics techniques covered are also useful for other domains.

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Section: Generative Modelsmentioning

confidence: 99%

Section: Preferential Attachmentmentioning

confidence: 99%

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Workload Modeling for Computer Systems Performance Evaluation

Feitelson

2015

191

131

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“…N ∝ T , indicating that the appearance probability of new users is a constant, α = N/T . According to the Simon model [25], based on linear preferential selection and constant appearance probability of new users, the complementary cumulative distributions of the numbers of sent invitations and received invitations for the users of Wealink follow a power law P c (n) ∼ n −( 1 1−α ) . Based on empirical data, for the inviters, we obtain α = 0.53 and P c (n) ∼ n −2.13 , and for the receivers, α = 0.35 and P c (n) ∼ n −1.54 .…”

Section: Preferential Selectionmentioning

confidence: 99%

How people make friends in social networking sites—A microscopic perspective

Wang

2012

Physica A: Statistical Mechanics and its Applications

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We study the detailed growth of a social networking site with full temporal information by examining the creation process of each friendship relation that can collectively lead to the macroscopic properties of the network. We first study the reciprocal behavior of users, and find that link requests are quickly responded to and that the distribution of reciprocation intervals decays in an exponential form. The degrees of inviters/accepters are slightly negatively correlative with reciprocation time. In addition, the temporal feature of the online community shows that the distributions of intervals of user behaviors, such as sending or accepting link requests, follow a power law with a universal exponent, and peaks emerge for intervals of an integral day. We finally study the preferential selection and linking phenomena of the social networking site and find that, for the former, a linear preference holds for preferential sending and reception, and for the latter, a linear preference also holds for preferential acceptance, creation, and attachment. Based on the linearly preferential linking, we put forward an analyzable network model which can reproduce the degree distribution of the network. The research framework presented in the paper could provide a potential insight into how the micro-motives of users lead to the global structure of online social networks.

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“…Historically, a discussion for the origin of skew distribution that appears in sociological, biological, and economic phenomena goes back to the Simon's stochastic model [1]. At the beginning of this century, the evidences of fat-tail degree distribution have been also observed in many real networks [2] through computer analyses for large data.…”

Section: Introductionmentioning

confidence: 99%

Combinatorial and approximative analyses in a spatially random division process

Hayashi

Komaki

Ide

et al. 2013

Physica A: Statistical Mechanics and its Applications

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For a spatial characteristic, there exist commonly fat-tail frequency distributions of fragment-size and -mass of glass, areas enclosed by city roads, and pore size/volume in random packings. In order to give a new analytical approach for the distributions, we consider a simple model which constructs a fractal-like hierarchical network based on random divisions of rectangles. The stochastic process makes a Markov chain and corresponds to directional random walks with splitting into four particles. We derive a combinatorial analytical form and its continuous approximation for the distribution of rectangle areas, and numerically show a good fitting with the actual distribution in the averaging behavior of the divisions.

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On a Class of Skew Distribution Functions

Cited by 1,852 publications

References 10 publications

Workload Modeling for Computer Systems Performance Evaluation

Workload Modeling for Computer Systems Performance Evaluation

How people make friends in social networking sites—A microscopic perspective

Combinatorial and approximative analyses in a spatially random division process

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