Stochastic comparisons of order statistics from heterogeneous populations, with applications in reliability

“…Some interesting partial ordering results on order statistics and spacings from independent but non-identically random variables have been obtained by Pledger and Proschan (1971), Proschan and Sethuraman (1976), Bapat and Kochar (1994), Boland, El-Neweihi, and Proschan (1994 ), Kochar and Kirmani (1995), Kochar and Korwar (1996), Kochar and Rojo (1996), Dykstra, Kochar, and Rojo (1997), Kochar and Ma (1999), Bon and Paltanea (1999), Kochar (1999), Khaledi and Kochar (1999), , and Khaledi and Kochar (2001).…”

Section: Introductionmentioning

confidence: 99%

Stochastic Orderings among Order Statistics and Sample Spacings

Khaledi¹,

Kochar

2002

Uncertainty and Optimality

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In this paper we review some of the results obtained recently in the area of stochastic comparisons of order statistics and sample spacings. We consider the cases when the parent observations are identically as well as non-identically distributed. But most of the time we shall be assuming that the observations are independent. The case of independent exponentials with unequal scale parameters is discussed in detail.

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“…Subsequently, Proschan and Sethuraman [55] strengthened this result from the componentwise stochastic ordering to the multivariate stochastic ordering. That is, under the assumptions of Theorem 2.1.1, they proved that…”

Section: Introductionmentioning

confidence: 99%

“…It is of great interest to investigate the effect of the change in the parameters of X i 's on the system lifetime. Ignoring the heterogeneity leads to underestimating the average failure rate of components as pointed out in Proschan and Sethuraman [55].…”

Section: Introductionmentioning

confidence: 99%

Stochastic Orders in Heterogeneous Samples with Applications

Xu¹

2000

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The statistics literature has mostly focused on the case when the data available is in the form of a random sample. In many cases, the observations are not identically distributed. Such samples are called heterogeneous samples. The study of heterogeneous samples is of great interest in many areas, such as statistics, econometrics, reliability engineering, operation research and risk analysis.Stochastic orders between probability distributions is a widely studied concept. There are several kinds of stochastic orders that are used to compare different aspects of probability distributions like location, variability, skewness, dependence, etc.In this dissertation, most of the work is devoted to investigating the properties of statistics based on heterogeneous samples with the aid of stochastic orders. We will see the effect of the change in the stochastic properties of various functions of observations as their parameters change. The theory of majorization will be used for this purpose.First, order statistics from heterogeneous samples will be investigated. Order statistics appear everywhere in statistics and related areas. The k-out-of-n systems are building blocks of a coherent system. The lifetime of such a system is the same as that of the (n−k +1)th order statistic in a sample size of n. Stochastic comparisons between order statistics have been studied extensively in the literature in case the parent observations are independent and identically distributed. The work in this dissertation has significant applications in many diverse areas of applied probability and statistics. For example, statistics based on order statistics and spacings from heterogeneous samples arise in studying the robust properties of statistical procedures; the work on order statistics will also provide a better estimation of lifetime of a coherent system in reliability engineering; convolution results will be of great interest in insurance and actuarial science for evaluating risks.

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Stochastic comparisons of order statistics from heterogeneous populations, with applications in reliability

Cited by 131 publications

References 3 publications

Convolution of Heterogeneous Bernoulli Random Variables and Some Applications

Convolution of Heterogeneous Bernoulli Random Variables and Some Applications

Stochastic Orderings among Order Statistics and Sample Spacings

Stochastic Orders in Heterogeneous Samples with Applications

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