Estimation of the Jump-Point in a Hazard Function

Abdel-Aty Yahia and Ferger Dietmar
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Abdel-Aty Yahia: Department of Mathematics, Faculty of Science, Al-Azhar University, 1884 Nasr City, Cairo, Egypt
Ferger Dietmar: Department of Mathematics, Dresden University of Technology, Mommsenstr. 13, D-01062 Dresden, Germany

Stochastics and Quality Control, 2003, vol. 18, issue 2, 251-261

Abstract: We consider a piecewise constant hazard function with exactly one jump point, say τ. It uniquely determines an Exponential distribution whose density features a discontinuity of the first kind at the change point τ. Assuming that τ is the unknown parameter of interest, the maximum likelihood estimator is shown to be strongly consistent for τ. Its computation is very simple, because it requires merely a finite number of comparisons. Some graphics and calculations illustrate our results.

Date: 2003
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DOI: 10.1515/EQC.2003.251

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