CHARACTERIZATIONS OF THE EXPONENTIAL DISTRIBUTION BY ORDER STATISTICS AND CONDITIONAL

Title & Authors
CHARACTERIZATIONS OF THE EXPONENTIAL DISTRIBUTION BY ORDER STATISTICS AND CONDITIONAL
Lee, Min-Young; Chang, Se-Kyung; Jung, Kap-Hun;

Abstract
Let X$\small{_1}$, X$\small{_2}$‥‥,X$\small{\_}$n/ be n independent and identically distributed random variables with continuous cumulative distribution function F(x). Let us rearrange the X's in the increasing order X$\small{\_}$1:n/ $\small{\leq}$ X$\small{\_}$2:n/ $\small{\leq}$ ‥‥ $\small{\leq}$ X$\small{\_}$n:n/. We call X$\small{\_}$k:n/ the k-th order statistic. Then X$\small{\_}$n:n/ - X$\small{\_}$n-1:n/ and X$\small{\_}$n-1:n/ are independent if and only if f(x) = 1-e(equation omitted) with some c > 0. And X$\small{\_}$j/ is an upper record value of this sequence lf X$\small{\_}$j/ > max(X$\small{_1}$, X$\small{_2}$,¨¨ ,X$\small{\_}$j-1/). We define u(n) = min(j|j > u(n-1),X$\small{\_}$j/ > X$\small{\_}$u(n-1)/, n $\small{\geq}$ 2) with u(1) = 1. Then F(x) = 1 - e(equation omitted), x > 0 if and only if E[X$\small{\_}$u(n+3)/ - X$\small{\_}$u(n)/ | X$\small{\_}$u(m)/ = y] = 3c, or E[X$\small{\_}$u(n+4)/ - X$\small{\_}$u(n)/|X$\small{\_}$u(m)/ = y] = 4c, n m+1.
Keywords
absolutely continuous distribution;characterization;conditional expectation;order statistic record value;
Language
English
Cited by
1.
CHARACTERIZATIONS OF THE LOMAX, EXPONENTIAL AND PARETO DISTRIBUTIONS BY CONDITIONAL EXPECTATIONS OF RECORD VALUES,;;

충청수학회지, 2009. vol.22. 2, pp.149-153
2.
CHARACTERIZATION OF CONTINUOUS DISTRIBUTIONS THROUGH RECORD STATISTICS,;;;

대한수학회논문집, 2010. vol.25. 3, pp.485-489
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