ON CHARACTERIZATION OF THE GAMMA DISTRIBUTION.
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1968
- Accession Number
- AD0669463
Entities
People
- Gordon Simons
- W. J. Hall
Organizations
- Stanford University