Journal ArticleDOI
Probability of ties and Markov property in discrete order statistics
Pushpa L. Gupta,Ramesh C. Gupta +1 more
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TLDR
In this paper, it is shown that, in the discrete case, the Markov property does not hold good and that the probability of ties is not equal to zero in the continuous case, whereas it is not true when the distribution is discrete.About:
This article is published in Journal of Statistical Planning and Inference.The article was published on 1981-01-01. It has received 6 citations till now. The article focuses on the topics: Markov property & Discrete phase-type distribution.read more
Citations
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Journal ArticleDOI
Order Statistics from Discrete Distributions
TL;DR: A survey of results on order statistics of a random sample taken from a discrete population is given in this article, where the authors discuss finite sample distribution theory and characterization results, and study the dependence structure.
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On the Markov property of order statistics
TL;DR: In this article, a necessary and sufficient condition for the order statistics to form a Markov chain for (n ≥ 3) is that there does not exist any atom x 0 of the parent distribution F satisfying F(x 0-)>0 and F (x 0)<1.
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On the non-Markovian structure of discrete order statistics
TL;DR: In this paper, it was shown that the Markov property holds for order statistics while sampling from a discrete parent population if and only if the population has at most two distinct units.
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Two remarks on order statistics
TL;DR: In this article, it was shown that the order statistics of general distributions have a certain Markov property for general distributions and that order statistics have monotone conditional regression dependence, which is well known in the case of continuous distributions.
Journal ArticleDOI
Characterization of discrete populations through conditional expectations of order statistics
Manuel Franco,José M. Ruiz +1 more
TL;DR: In this paper, the expected values of any order statistic when one of its adjacent order statistics is known (order mean function) from a sequence of sizen of independent and identically distributed random variables with discrete distribution are given.
References
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Book ChapterDOI
Characterizations of Probability Distributions by Properties of Order Statistics I
TL;DR: In this paper, the authors attempt to unify and somewhat extend the theory of characterizing probability distributions by properties of order statistics, and discuss the major directions of characterizations for univariate continuous distributions.
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A Characteristic Property of the Exponential Distribution
TL;DR: In this paper, a necessary and sufficient condition for exponential nonnegative random variables to be exponential is given which involves the identical distribution of the random variables $X$ and $(n - i) (X_{i+1,n} - X_{i,n})$ for some $i$ and $n$, $(1 \leqq i < n)$.
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Characterization of the exponential and power distributions
TL;DR: In this article, the exponential and power distributions were characterized in the class of all nontrivial distributions, and the exponential distribution was characterized in terms of all non-uniform distributions.
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Two Characterizations of the Geometric Distribution
TL;DR: In this article, a weak characterizing property of the geometric distribution is shown, i.e., a very weak form of this property is a characterising property of geometric distribution, and other characterizations are also obtained by similar properties.