Characterization of Discrete Probability Distributions by Partial Independence.
Abstract
If X and Y are random variables such that P (X > Y) = 1 and the conditional distribution of Y given X is binomial, then Moran (1952) showed that Y and (X-Y) are independent if X is Poisson. This document extends Moran's result to a more general type of conditional distribution of Y given X, using only partial independence of Y and X-Y. This provides a generalization of a recent results of Janardhan and Rao (1982) on the characterization of generalized Polya-Eggenberger distribution. A variant of Moran's theorem is proved which generalizes the results of Patil and Seshadri (1964) on the characterization of the distribution of a random variable x based on some conditions on the conditional distribution of Y given X and the independence of Y and X-Y.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1985
- Accession Number
- ADA160130
Entities
People
- A. A. Alzaid
- Calyampudi Radhakrishna Rao
- D. N. Shanbhag
Organizations
- University of Pittsburgh