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ON THE DISTRIBUTIONS OF ORDER STATISTICS FOR A RANDOM SAMPLE SIZE *
Author(s) -
Consul P.C.
Publication year - 1984
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.1467-9574.1984.tb01115.x
Subject(s) - mathematics , statistics , poisson distribution , order statistic , negative binomial distribution , exponential family , exponential distribution , random variable , sample size determination , binomial (polynomial) , binomial distribution , univariate distribution
The probability distribution of the i –th and j –th order statistics and of the range R of a sample of size n , taken from a population with probability density function f (x ) have been obtained when the sample size n is a random variable N and has: (i) a generalized Poisson distribution; and (ii) a generalized negative bonimial distribution. Specific results are then obtained; (a) when f (x) is uniform over (0,1); and (b) when f(x) is exponential. All the results for N , being a Poisson, binomial and negative binomial rv follow as special cases.