
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 distributionfree 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