期刊名称：Sankhya. Series A, mathematical statistics and probability
印刷版ISSN：0976-836X
电子版ISSN：0976-8378
出版年度：2003
卷号：65
期号：04
出版社：Indian Statistical Institute
摘要：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 $\tilde e$ if $x*\tilde e= x.$ 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.
关键词：Characterization, almost lack of memory property, strong Markov property, periodic failure rate, binary associative operation, exponential distribution.
