The Annals of Statistics

Mixtures of Exponential Distributions

Nicholas P. Jewell

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist., Volume 10, Number 2 (1982), 479-484.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345789

Digital Object Identifier
doi:10.1214/aos/1176345789

Mathematical Reviews number (MathSciNet)
MR653523

Zentralblatt MATH identifier
0495.62042

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation
Secondary: 62N05: Reliability and life testing [See also 90B25]

Keywords
Mixtures survival distributions Weibull distributions exponential distributions maximum likelihood consistency EM algorithm

Citation

Jewell, Nicholas P. Mixtures of Exponential Distributions. Ann. Statist. 10 (1982), no. 2, 479--484. doi:10.1214/aos/1176345789. https://projecteuclid.org/euclid.aos/1176345789


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