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Characterization of pareto distribution through expectation

Author Affiliations

  • 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)

Abstract

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.

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