ON THE DISTRIBUTIONS OF ORDER STATISTICS FOR A RANDOM SAMPLE SIZE*

P.C. Consul

Statistica Neerlandica, 1984, vol. 38, issue 4, 249-256

Abstract: 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.

Date: 1984
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