Characterization of pareto distribution through expectation
- 1Department of Statistics, Sardar Patel University, V.V. Nagar-388120, Gujarat, India
Res. J. Mathematical & Statistical Sci., Volume 5, Issue (2), Pages 1-4, February,12 (2017)
In statistical inference we often encounter the situation, for instant 60 observations of random phenomena observed and one group of students fit normal distribution whereas other group fits log-normal distribution with almost same p-value. This is one of cases where characterization results provide navigation tools for correct direction for further study (research). One of the research materials which receives room in both pure (mathematics) and applied (probability) is characterization rules because they are boundary points of both. That is why mathematical community as well as probabilists and statisticians contribute research are of characterizations. Characterization is not concern to academician or researcher only who deals with foundation and application of probabilistic model building but also concern to operation research, behavior science, natural science, decision making process in industrial and engineering problem. For characterization of Pareto distribution one needs any arbitrary non constant function only by approach of identity of distribution and equality of expectation of function of random variable in place of approaches such as relation (linear) in (economic variation) reported and true income, independency of suitable function of order statistics, mean and the extreme observation of the sample etc. Examples are given for illustrative purpose.
- Krishnaji N. (1970)., Characterization of the Pareto Distribution Through a Model of Underreported Incomes., Econometrica, 38(2), 251-255.
- Nagesh S.R., Michael J.H. and Marcello P. (1974)., A Characterization of the Pareto Distribution., The Annals of Statistics, 2(3), 599-601.
- Malik Henrick John (1970)., A characterization of the Pareto distribution., Scandinavian Actuarial Journal, 3(4), 115-117.
- Ahsanullah M. and Kabir A.B.M. (1973)., A characterization of the Pareto distribution., Canadian Journal of Statistics, 1(1-2), 109-112.
- Ahsanullah M., Lutful Kabir A.B.M. (1974)., Characterization of the Pareto distribution., Communication in statistics, 3(10), 953-957.
- Shah S.M. and Kabe D.G. (1981)., Characterizations of Exponential, Pareto, Power Function, BURR and Logistic Distributions by Order Statistics., Biometrical Journal, 23(2), 141-146.
- Dimaki C. and Xekalaki Evdokia (1993)., Characterizations of the Pareto distribution based on order statistics., Stability Problems for Stochastic Models, Lecture Notes in Mathematics, 1546, 1-16.
- Srivastava M.S. (1965)., Characterizations of Pareto’s Distributions and ., Ann. Math. Statist., 36, 361-362.
- Beg M.L. and Kirmani S.N.U.A. (1974)., On a characterization of exponential and related distributions., Austral. J. Statist., 16 (3), 163-166.
- Dallas A.C. (1976)., Characterization Pareto and power distribution., Ann. Ins. Statist. Math, 28(1), 491-497.
- Ali M.A. and Khan A.H. (1998)., Characterization of Some Types of Distributions, Information and Management Sciences, 9(2), 1-9.
- Tavangar M. and Asadi M. (2011)., Some new characterization results on exponential and related distributions, Bulletin of the Iranian Mathematical Society, 36(1), 257-272.