Accession Number : AD0619501

Title :   ON THE BIVARIATE MOMENTS OF ORDER STATISTICS FROM A LOGISTIC DISTRIBUTION AND APPLICATIONS.

Descriptive Note : Technical rept.

Corporate Author : PURDUE UNIV LAFAYETTE IND DEPT OF STATISTICS

Personal Author(s) : Shah,B. K.

Report Date : JUL 1965

Pagination or Media Count : 31

Abstract : Let x(1),x(2),...,x(n) be an ordered sample of n independent and identically distributed random variables from a Logistic Distribution whose cumulative distribution function is 1/(1+exp(-x)). In this paper several results are obtained for a simple Beta distribution whose density function is x to the (l-1) power (1-x) to the (m-1) power, 0 < or = x < or = 1. Using these results the exact value of the covariance of the lth and mth order statistics is obtained in terms of the diagamma and trigamma functions. Recurrence relations of the covariance of (l+1)th, and (m+1)th order statistics from a sample of size (n+1) in terms of the lower order covariances and moments are obtained. These relations are useful for the formal solutions of various problems of determination of best linear combinations of order statistics for various estimation problems concerning parameters of a logistic distribution. Table of covariances of all pairs of order statistics for n < or = 10 is given. (Author)

Descriptors :   (*STATISTICAL DISTRIBUTIONS, ANALYSIS OF VARIANCE), (*ANALYSIS OF VARIANCE, STATISTICAL DISTRIBUTIONS), PROBABILITY, SAMPLING, INTEGRALS

Distribution Statement : APPROVED FOR PUBLIC RELEASE