Characterizations of the Exponential Distribution by Relevation Type Equations.
TLDR
In this article, two characterizations of the exponential distribution are discussed, based on a generalization of the lack of memory property, motivated by the notion of relevance of distributions introduced by Krakowski (1973).Abstract:
: In this note two characterizations of the exponential distribution are discussed, based on a generalization of the lack of memory property. These results were motivated by the notion of 'relevation of distributions' introduced by Krakowski (1973). (Author)read more
Citations
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Reliability applications of the relevation transform
TL;DR: In this article, it was shown that Krakowski's relevation transform generates the nonhomogeneous Poisson process in an analogous fashion to the way in which Stieltjes convolution generates the renewal process.
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Recent results on characterization of probability distributions: a unified approach through extensions of deny's theorem
TL;DR: In this article, the authors review some of the recent contributions to characterization of probability distributions and show how improved versions of these results follow as immediate corollaries to LRS theorems.
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Characterization of the exponential distribution by the relevation transform
Ka-Sing Lau,B. L. S. Prakasa Rao +1 more
TL;DR: In this paper, an improved version of the result in Grosswald et al. (1980) was obtained by using the relevation transform introduced by Krakowski (1973), which was then used to obtain a characterization of the exponential distribution.
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Probability distributions in periodic random environment and their applications
TL;DR: Periodic random environments and mechanisms of their effect on imbedded random variables are discussed, and nonstationary Poisson processes with periodic failure rates appear to be the closest extension of the homogeneous Poisson process to model the number of events imbedding into random environment of p...
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Renewal and nonhomogeneous Poisson processes generated by distributions with periodic failure rate
TL;DR: In this article, two renewal processes, known in reliability maintenance as minimal repair and replacement policy, are considered and their properties are studied in the case where the generating random sequence has a distribution with periodic failure rate.
References
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The relevation transform and a generalization of the gamma distribution function
TL;DR: Survival models arising in mathematical demography, in renewal and in replacement models lead to a generalization of the Gamma distribution function, which corresponds to the addition of random variables, generally dependent on reîevation product.
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On a characterization of the exponential distribution by spacings
TL;DR: In this article, the smallest order statistics in a random sample of sizen from a non-negative random variable with probability distribution function F is defined and a necessary and sufficient condition for F to be exponential is given which involves the identical distribution of the random variables.