Characterization of probability distributions via binary associative operation

Muliere, Pietro ; Prakasa Rao, B. L. S. (2003) Characterization of probability distributions via binary associative operation Sankhya - Series A, 65 (4). pp. 799-806. ISSN 0581-572X

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Official URL: http://www.jstor.org/pss/25053314

Abstract

A binary operation * over real numbers is said to be associative if (x * y) * z = x * (y * z) and it is said to be reducible if x * y = x * z or y * w = z * w if and only if z = y. The operation * is said to have an identity element ẽ if x * ẽ = x. We characterize different classes of probability distributions under such binary operations between random variables. Further more we characterize distributions with the almost lack of memory property or with the strong Markov property or with the periodic failure rate under such a binary operation extending the results for exponential distributions under addition operation as binary operation.

Item Type:Article
Source:Copyright of this article belongs to Indian Statistical Institute.
ID Code:37685
Deposited On:26 Apr 2011 12:46
Last Modified:26 Apr 2011 12:46

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