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Characteristic properties of order statistics based on random sample size from an exponential distribution
Author(s) -
Ahsanullah M.
Publication year - 1988
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.1988.tb01233.x
Subject(s) - mathematics , order statistic , random variable , statistics , exponential function , combinatorics , order (exchange) , sample size determination , exponential distribution , probability density function , distribution (mathematics) , integer (computer science) , population , mathematical analysis , finance , economics , demography , sociology , computer science , programming language
Suppose X 1 , X 2 , X m is a random sample of size m from a population with probability density function f (x), x > 0), and let X 1, m < × 2, m <… < X m, m be the corresponding order statistics. We assume m is an integer‐valued random variable with P( m = k ) = p (1‐ p ) k‐1 , k = 1,2,… and 0 < p < 1. Two characterizations of the exponential distribution are given based on the distributional properties of X l, m .