On the Distribution of a Symmetric Statistic from a Mixed Population
- 1 November 1972
- journal article
- research article
- Published by JSTOR in Technometrics
- Vol. 14 (4) , 919
- https://doi.org/10.2307/1267140
Abstract
The density of a symmetric statistic T = g(X 1, X 2, …, Xn ), for a random sample from a mixed population with density f(x) = pf 1(x) + pf 2), is a binomial mixture of the densities of the statist.ics Tk = g(Xk1 , Xk2 , Xkn ), k = 0, 1, … n. where Xki 's are independent with density f 1(x) if i ≤ k and density f 2(x) if i > k. It is shown how to find the distributions of some important symmetric statistics like sample mean, sample variance, and order statistics by using Tk 's. The results are applied to normal and exponential mixtures.Keywords
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