Power law distributions are an increasingly common model for computer science applications; for example, they have been used to describe le size distributions and in- and out-degree distributions for the Web and Internet graphs. Recently, the similar lognormal distribution has also been suggested as an appropriate alternative model for le size distributions. In this paper, we brie
y survey some of the history of these distributions, focusing on work in other elds. We nd that several recently proposed models have antecedents in work from decades ago. We also nd that lognormal and power law distributions connect quite naturally, and hence it is not surprising that lognormal distributions arise as a possible alternative to power law distributions. 1
|
754
|
The Pricing of Options and Corporate Liabilities
– Black, Scholes
- 1973
|
|
699
|
On power-law relationship of the internet topology
– FALOUTSOS, FALOUTSOS, et al.
- 1999
|
|
557
|
Generating Representative Web Workloads for Network and Server Performance Evaluation
– Barford, Crovella
- 1998
|
|
196
|
The Web as a graph: Measurements, models, and methods
– Kleinberg, Kumar, et al.
- 1999
|
|
153
|
Changes in Web client access patterns: characteristics and caching implications
– Barford, Bestavros, et al.
- 1999
|
|
134
|
Stochastic models for the web graph
– Kumar, Raghavan, et al.
- 2000
|
|
124
|
On the origin of power laws in internet topologies
– Medina, Matta, et al.
- 2000
|
|
97
|
Heavy-Tailed Probability Distributions in the World Wide Web”. In A Practical Guide to Heavy Tails
– Crovella, Taqqu, et al.
- 1998
|
|
94
|
Self-similarity in world wide Web trac: Evidence and possible causes
– Crovella, Bestavros
- 1997
|
|
90
|
Mean-field theory for scale-free random networks
– Barabasi, Albert, et al.
- 1999
|
|
87
|
Cours d’Economie Politique
– Pareto
- 1896
|
|
85
|
On a class of skew distribution functions
– Simon
- 1955
|
|
83
|
Graph structure in the web: experiments and models
– Border, Kumar, et al.
|
|
73
|
Wide-area trac: the failure of Poisson modeling
– Paxson, Floyd
- 1995
|
|
56
|
On a general model of Web graphs
– Cooper, Frieze
|
|
55
|
Selected Studies of the Principle of Relative Frequency in Language
– Zipf
- 1932
|
|
50
|
The diameter of scale-free random graph
– Bollobás, Riordan
|
|
50
|
On the self-similar nature of ethernet trac
– Leland, Taqqu, et al.
- 1994
|
|
49
|
Fractals and Scaling in Finance
– Mandelbrot
- 1997
|
|
46
|
Random texts exhibit Zipf’s-law-like word frequency distribution
– Li
- 1992
|
|
40
|
A mathematical theory of evolution based on the conclusions of Dr
– Yule
- 1925
|
|
39
|
Connectivity of growing random networks
– Krapivsky, Redner, et al.
- 2000
|
|
39
|
The Self-Organizing
– Krugman
- 1996
|
|
39
|
An informational theory of the statistical structure of languages
– Mandelbrot
- 1953
|
|
36
|
A survey of recursive trees
– Smythe, Mahmoud
- 1995
|
|
35
|
The Lognormal Distribution
– Aitchison, Brown
- 1957
|
|
35
|
Human Behavior and the Principle of Least Eort
– Zipf
- 1949
|
|
34
|
The Psycho-Biology of Language: An Introduction to Dynamic Philology
– Zipf
- 1935
|
|
33
|
Growth dynamics of the world wide web
– ADAMIC, A
- 1999
|
|
27
|
Variations on random graph models of the Web
– Drinea, Enachescu, et al.
|
|
27
|
Extracting large scale knowledge bases from the Web
– Kumar, Raghavan, et al.
- 1999
|
|
20
|
The double Pareto-lognormal distribution - A new parametric model for size distribution. 2001. Available at http://www.math.uvic.ca/faculty/reed/index.html
– Reed
- 2001
|
|
20
|
Heavy tails, generalized coding, and optimal web layout
– Zhu, Yu, et al.
- 2001
|
|
19
|
The nature of markets in the World Wide Web
– Adamic, Huberman
- 2000
|
|
18
|
Zipf’s law for cities: An explanation
– Gabaix
- 1999
|
|
17
|
A model of income distribution
– Champernowne
- 1953
|
|
17
|
Option pricing: a simpli approach
– Cox, Ross, et al.
- 1979
|
|
15
|
Some Further Notes on a Class of Skew Distribution Functions
– Simon
- 1960
|
|
14
|
Random dierence equations and renewal theory for products of random matrices
– Kesten
- 1973
|
|
14
|
A Note on a Class of Skew Distribution Functions: Analysis and Critique of a Paper by
– Mandelbrot
- 1959
|
|
14
|
On 1/f noise and other distributions with long tails
– Montroll, Shlesinger
- 1982
|
|
13
|
Maximum Entropy Formalism, Fractals, Scaling Phenomena, and 1/f Noise: A Tale of Tails
– Montroll, Shlesinger
- 1983
|
|
11
|
Das Gesetz der Bevölkerungskonzentration. Petermanns Geographische Mitteilungen 59
– Auerbach
- 1913
|
|
9
|
Lognormal Distributions: Theory and Application
– Crow, Shimizu
- 1988
|
|
9
|
The structural cause of size distributions
– Downey
- 2000
|
|
9
|
Zipf’s law, the central limit theorem, and the random division of the unit interval
– Perline
- 1996
|
|
6
|
Gammes Stenographiques. Institut Stenographique de
– Estoup
- 1916
|
|
5
|
On criteria for descriptions of income distribution
– Aitchison, Brown
- 1954
|
|
5
|
Stochastic dynamics modeling of the protein sequence length distribution in genomes: implications for microbial evolution
– Jain, Ramakumar
- 1999
|
|
5
|
The frequency distribution of scienti productivity
– Lotka
- 1926
|
