A discrete truncated Pareto distribution

Abstract We propose a new discrete distribution with finite support, which generalizes truncated Pareto and beta distributions as well as uniform and Benford’s laws. Although our focus is on basic properties and stochastic representations, we also consider parameter estimation and include an illustration from ecology showing potential applications of this new stochastic model.

[1]  I. Linkov,et al.  Integrating Risk and Resilience Approaches to Catastrophe Management in Engineering Systems , 2013, Risk analysis : an official publication of the Society for Risk Analysis.

[2]  D. Clayton,et al.  Population biology of swift (Apus apus) ectoparasites in relation to host reproductive success , 1995 .

[3]  Pramendra Singh Pundir,et al.  Discrete Burr and discrete Pareto distributions , 2009 .

[4]  Mário Almeida-Neto,et al.  An integrated framework to improve the concept of resource specialisation. , 2014, Ecology letters.

[5]  R. Ricklefs,et al.  Host specificity of Lepidoptera in tropical and temperate forests , 2007, Nature.

[6]  R. Ricklefs,et al.  The global distribution of diet breadth in insect herbivores , 2014, Proceedings of the National Academy of Sciences.

[7]  T. Hill A Statistical Derivation of the Significant-Digit Law , 1995 .

[8]  George Kingsley Zipf,et al.  Human behavior and the principle of least effort , 1949 .

[9]  Michael Lynch,et al.  The Origins of Genome Architecture , 2007 .

[10]  C. Kapadia,et al.  On estimating the parameter of a truncated geometric distribution by the method of moments , 1975 .

[11]  J. Fordyce,et al.  A Hierarchical Bayesian Approach to Ecological Count Data: A Flexible Tool for Ecologists , 2011, PloS one.

[12]  Michael Muskulus,et al.  Fluctuations and determinism of respiratory impedance in asthma and chronic obstructive pulmonary disease. , 2010, Journal of applied physiology.

[13]  T. Kozubowski,et al.  Discrete Pareto Distributions , 2014 .

[14]  Sarah F. Tebbens,et al.  Upper-truncated Power Laws in Natural Systems , 2001 .

[15]  W. Reed The Pareto, Zipf and other power laws , 2001 .

[16]  James C. Stegen,et al.  Variation in above-ground forest biomass across broad climatic gradients , 2011 .

[17]  M. E. J. Newman,et al.  Power laws, Pareto distributions and Zipf's law , 2005 .

[18]  N. Balakrishnan,et al.  A Primer on Statistical Distributions , 2003 .

[19]  S. M. Burroughs,et al.  The Upper-Truncated Power Law Applied to Earthquake Cumulative Frequency-Magnitude Distributions: Evidence for a Time-Independent Scaling Parameter , 2002 .

[20]  D. Sornette Multiplicative processes and power laws , 1997, cond-mat/9708231.

[21]  R. Sandland A NOTE ON SOME APPLICATIONS OF THE TRUNCATED GEOMETRIC DISTRIBUTION , 1974 .

[22]  C. Kapadia,et al.  On estimating the parameter of a truncated geometric distribution , 1968 .

[23]  A. W. Kemp,et al.  Univariate Discrete Distributions , 1993 .

[24]  Evolution of Surnames , 1991 .

[25]  Mark E. J. Newman,et al.  Power-Law Distributions in Empirical Data , 2007, SIAM Rev..

[26]  K. Krishnamoorthy Handbook of statistical distributions with applications , 2006 .

[27]  P. Kroupa,et al.  The influence of multiple stars on the high-mass stellar initial mass function and age-dating of young massive star clusters , 2008, 0811.3730.

[28]  Lester Lipsky,et al.  The Importance of Power-Tail Distributions for Modeling Queueing Systems , 1999, Oper. Res..

[29]  S. M. Burroughs,et al.  UPPER-TRUNCATED POWER LAW DISTRIBUTIONS , 2001 .

[30]  M. Meerschaert,et al.  Parameter Estimation for the Truncated Pareto Distribution , 2006 .

[31]  Theodore P. Hill The First Digit Phenomenon , 1998 .

[32]  Benjamin M. Bolker,et al.  Ecological Models and Data in R , 2008 .

[33]  S. Galeotti,et al.  K-T boundary extinction: Geologically instantaneous or gradual event? Evidence from deep-sea benthic foraminifera , 1994 .

[34]  Jordi Bascompte,et al.  Plant-Animal Mutualistic Networks: The Architecture of Biodiversity , 2007 .

[35]  W. Reed,et al.  From gene families and genera to incomes and internet file sizes: why power laws are so common in nature. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.