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 non-identically 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