The Annals of Statistics

Maximum Likelihood Estimation of a Compound Poisson Process

Leopold Simar

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Abstract

The problem of estimating the compounding distribution of a compound Poisson process from independent observations of the compound process has been analyzed by Tucker (1963). A maximum likelihood method is proposed. The existence, uniqueness and convergence of the resulting estimator are derived. One obtains practical solutions by means of a very simple algorithm which is briefly described. A numerical example is presented in the risk business framework.

Article information

Source
Ann. Statist. Volume 4, Number 6 (1976), 1200-1209.

Dates
First available: 12 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aos/1176343651

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aos/1176343651

Mathematical Reviews number (MathSciNet)
MR428582

Zentralblatt MATH identifier
0362.62095

Subjects
Primary: 62G05: Estimation
Secondary: 62M99: None of the above, but in this section

Keywords
Compound Poisson process mixed Poisson process maximum likelihood method risk business

Citation

Simar, Leopold. Maximum Likelihood Estimation of a Compound Poisson Process. The Annals of Statistics 4 (1976), no. 6, 1200--1209. doi:10.1214/aos/1176343651. http://projecteuclid.org/euclid.aos/1176343651.


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