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June, 1982 Mixtures of Exponential Distributions
Nicholas P. Jewell
Ann. Statist. 10(2): 479-484 (June, 1982). DOI: 10.1214/aos/1176345789


Arbitrary nonparametric mixtures of exponential and Weibull (fixed shape) distributions are considered as possible models for a lifetime distribution. A characterization of such distributions is given by the well-known characterization of Laplace transforms. The maximum likelihood estimate of the mixing distribution is investigated and found to be supported on a finite number of points. It is shown to be unique and weakly convergent to the true mixing measure with probability one. A practical algorithm for computing the maximum likelihood estimate is described. Its performance is briefly discussed and some illustrative examples given.


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Nicholas P. Jewell. "Mixtures of Exponential Distributions." Ann. Statist. 10 (2) 479 - 484, June, 1982.


Published: June, 1982
First available in Project Euclid: 12 April 2007

zbMATH: 0495.62042
MathSciNet: MR653523
Digital Object Identifier: 10.1214/aos/1176345789

Primary: 62G05
Secondary: 62N05

Keywords: consistency , EM algorithm , exponential distributions , maximum likelihood , mixtures , survival distributions , Weibull distributions

Rights: Copyright © 1982 Institute of Mathematical Statistics

Vol.10 • No. 2 • June, 1982
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