
Accession Number : AD0669463
Title : ON CHARACTERIZATION OF THE GAMMA DISTRIBUTION.
Descriptive Note : Technical rept.,
Corporate Author : STANFORD UNIV CALIF DEPT OF STATISTICS
Personal Author(s) : Hall,W. J. ; Simons,Gordon
Report Date : 01 MAY 1968
Pagination or Media Count : 15
Abstract : Let X sub 1, X sub 2,... be a sequence of i.i.d. random variables and S sub n = summation, j = 1 to j = n, of X sub j. If X sub 1 has a gamma distribution, (Z sub n is identically equal to S(subscript n, superscript r)/E(S subscript n, superscript r)); n = or > 1) is a reverse martingale sequence for any positive r. These reverse martingales find applications in sequential analysis. In this paper the converse is proved for any integer r > 1, and this provides a characterization of the gamma distribution; in fact, it is sufficient that the reverse martingale sequence have finite length r. Another characterization is also proved, extending the case r = 2 to nonidentically distributed r.v.'s. (Author)
Descriptors : (*STATISTICAL DISTRIBUTIONS, THEOREMS), RANDOM VARIABLES, SEQUENTIAL ANALYSIS, MATRICES(MATHEMATICS), SET THEORY
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE