Statistical inference for geometric processes with gamma distributions

A stochastic process { X i } is a geometric process if there exists a positive real number a such that { a i−1 X i } generates a renewal process. Under the assumption that X 1 follows a Gamma distribution, the statistical inference problem for the geometric process is studied. The parameters a, μ an...

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Bibliographic Details
Published in:Computational statistics & data analysis 2004-10, Vol.47 (3), p.565-581
Main Authors: Chan, Jennifer S.K., Lam, Yeh, Leung, Doris Y.P.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Geometric process
Mathematics
Maximum likelihood estimate
Moment estimate
Nonparametric inference
Parametric inference
Probability and statistics
Renewal process
Sciences and techniques of general use
Statistics
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Summary:A stochastic process { X i } is a geometric process if there exists a positive real number a such that { a i−1 X i } generates a renewal process. Under the assumption that X 1 follows a Gamma distribution, the statistical inference problem for the geometric process is studied. The parameters a, μ and σ 2, where μ and σ 2, are respectively, the mean and variance of X 1, are estimated by parametric methods including maximum likelihood method along with some nonparametric methods previously proposed by Y. Lam such as the modified moment method. Limiting distributions for the maximum likelihood estimators are derived and this enables us to construct confidence intervals and perform hypothesis testing on parameters. Then some suggestions on the choice of methods are made based on simulation experiments and real data analysis.
ISSN:0167-9473
1872-7352
DOI:10.1016/j.csda.2003.12.004