Accession Number : AD0664475

Title :   ON THE DISTRIBUTION OF THE MAXIMUM AND MINIMUM OF RATIOS OF ORDER STATISTICS.

Descriptive Note : Technical rept.,

Corporate Author : PURDUE UNIV LAFAYETTE IND DEPT OF STATISTICS

Personal Author(s) : Barlow,R. E. ; Gupta,S. S. ; Panchapakesan,S.

Report Date : DEC 1967

Pagination or Media Count : 26

Abstract : Let X sub i(i = 0,1,...,p) be (p + 1) independent and identically distributed nonnegative random variables each representing the jth order statistic in a random sample of size n from a continuous distribution G(x) of a nonnegative random variable. Let H sub (j,n) (x) be the cumulative distribution function of X sub i(i = 0,1,...,p). Consider the ratios Y sub i = X sub i/X sub o (i = 1,2,...,p). The random variables Y sub i (i = 1,2,...,p) are correlated and the distribution of the maximum and the minimum is of interest in problems of selection and ranking for restricted families of distribution. The distribution-free subset selection rules using the percentage points of these order statistics are investigated in a companion paper by Barlow and Gupta (1967). In the present paper, we discuss the distribution of these statistics, in general, for any G(x) and then derive specific results for G(x) = 1-(e to the power (-x/theta)), x > 0, theta > 0. Section 2 deals with the distribution of the maximum while Section 3 discusses the distribution of the minimum. Section 4 describes the tables of the percentage points of the two statistics. (Author)

Descriptors :   (*STATISTICAL ANALYSIS, TABLES(DATA)), RANDOM VARIABLES, SAMPLING, EXPONENTIAL FUNCTIONS, DISTRIBUTION FUNCTIONS, TRANSCENDENTAL FUNCTIONS, PROBABILITY

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE