Identification of Mixtures of Exponential Distributions by Means of a Predictor and Expectations of Order Statistics

El-Arishy, S. M.; Ahmed, A. N.

doi:10.14490/jjss1995.26.119

Cited by 5 publications

(1 citation statement)

References 9 publications

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“…An important characteristic of a Weibull distribution is that its failure rate is decreasing for < 1, constant for = 1, and increasing for > 1. Several characterizations of mixture of distributions (for example, exponential, hyperexponential, gompertz, Rayleigh, and generalized power function distributions) -based on conditional expectations of order statistics -have been extensively discussed by Nassar and Mahmoud (1985), Nassar (1988), El-Arishy and Ahmed (1996), Wu and Lee (1998a,b), , Navarro and Ruiz (2004), Nassar (2005Nassar ( , 2006, and Lee et al (2011). As for the characterizations of mixture of Weibull distributions, in this article we propose an extension of the results of Khan and Ali (1987).…”

Section: Introductionmentioning

confidence: 95%

Characterization of Mixtures of Weibull and Pareto Distributions Based on Conditional Expectation of Order Statistics

Lee¹,

Wu²,

Li³

2013

Communications in Statistics - Theory and Methods

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The mixture of Weibull random variables X 1 and X 2 are identified in terms of relations between the conditional expectation of X 2 2 − X 1 2 r given X 1 2 (or ( X 2 2 k given X 1 2 ∀ k ≤ r and hazard rate function of the distribution, where X 1 2 and X 2 2 denote the corresponding order statistics, r is a positive integer and > 0. In addition, by using the natural logarithm transformation, we also characterize and mixture of Pareto distributions based on the conditional expectation of order statistics. Furthermore, when the sample size is n, the above results are also valid, and we also give an application to Multi-Hit models of carcinogenesis (Parallel Systems). Finally, we also characterize mixture of Weibull and Pareto distributions based on the conditional expectation of upper record values.

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