The Moments of Log-Weibull Order Statistics
- 1 May 1969
- journal article
- research article
- Published by JSTOR in Technometrics
- Vol. 11 (2) , 373
- https://doi.org/10.2307/1267267
Abstract
Let X 1n ≤ X 2n ≤,…, ≤ Xnn be the order statistics of a random sample of size n. For any integrable function g(x) define E(i, n) = E(g(X in )) and M(n) = E(1, n) = E(g(X 1n )). A number of formulae expressing E(i, n) in terms of M(j), j ≤ n, are developed. For example, These results are applied to obtain the means and variances of the order statistics of a log-Weibull distribution (F(z) = 1 – exp (− exp x)). Tables of these means and variances are given for 1 ≤ i ≤ n, n = 1 (1) 50 (5) 100. The computations were made using a set of 100 decimal place logarithms of integers. Examples of the use of these tables in obtaining weighted least squares estimates from censored samples from a Weibull distribution are also given.Keywords
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