Parameter estimation in geometric process with Weibull distribution

We consider geometric process (GP) when the distribution of the first occurrence time of an event is assumed to be Weibull. Explicit estimators of the parameters in GP are derived by using the method of modified maximum likelihood (MML) proposed by Tiku [24]. Asymptotic distributions and consistency...

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Bibliographic Details
Published in:Applied mathematics and computation 2010-11, Vol.217 (6), p.2657-2665
Main Authors: Aydoğdu, Halil, Şenoğlu, Birdal, Kara, Mahmut
Format: Article
Language:English
Subjects:
Asymptotic normality
Asymptotic properties
Computer simulation
Consistency
Efficiency
Estimators
Exact sciences and technology
Geometric process
Mathematical analysis
Mathematical models
Mathematics
Modified likelihood
Monte Carlo methods
Monte Carlo simulation
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in probability and statistics
Sciences and techniques of general use
Taylor series
Weibull distribution
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Summary:We consider geometric process (GP) when the distribution of the first occurrence time of an event is assumed to be Weibull. Explicit estimators of the parameters in GP are derived by using the method of modified maximum likelihood (MML) proposed by Tiku [24]. Asymptotic distributions and consistency properties of these estimators are obtained. We show that our estimators are more efficient than the widely used modified moment (MM) estimators via Monte Carlo simulation study. Further, two real life examples are given at the end of the paper.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2010.08.003