CHARACTERIZATIONS OF THE LOMAX, EXPONENTIAL AND PARETO DISTRIBUTIONS BY CONDITIONAL EXPECTATIONS OF RECORD VALUES

Abstract

Let {Xn, n ≥ 1} be a sequence of independent and identically distributed random variables with absolutely continuous cumulative distribution function (cdf) F (x) and probability density function (pdf) f (x). Suppose XU (m),m = 1, 2, · · · be the upper record values of {Xn, n ≥ 1}. It is shown that the linearity of the conditional expectation of XU (n+2) given XU (n) characterizes the lomax, exponential and pareto distributions.

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