Testing of two sample proportional intensity assumption for non-homogeneous Poisson processes

For two independent non-homogeneous Poisson processes with unknown intensities we propose a test for testing the hypothesis that the ratio of the intensities is constant versus it is increasing on (0, t]. The existing test procedures for testing such relative trends are based on conditioning on the...

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Bibliographic Details
Published in:Journal of statistical planning and inference 1999-11, Vol.81 (2), p.237-251
Main Authors: Deshpande, J.V., Mukhopadhyay, M., Naik-Nimbalkar, U.V.
Format: Article
Language:English
Subjects:
Consistency
Exact sciences and technology
Innovation martingale
Intensity function
Martingale central limit theorem
Mathematics
Multivariate analysis
Nonparametric inference
Parametric inference
Probability and statistics
Repairable systems
Sciences and techniques of general use
Statistics
Trend comparison
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Summary:For two independent non-homogeneous Poisson processes with unknown intensities we propose a test for testing the hypothesis that the ratio of the intensities is constant versus it is increasing on (0, t]. The existing test procedures for testing such relative trends are based on conditioning on the number of failures observed in (0, t] from the two processes. Our test is unconditional and is based on the original time truncated data which enables us to have meaningful asymptotics. We obtain the asymptotic null distribution (as t becomes large) of the proposed test statistic and show that the proposed test is consistent against several large classes of alternatives. It was observed by Park and Kim (IEEE. Trans. Rehab. 40 (1), 1992, 107–111) that it is difficult to distinguish between the power-law and log-linear processes for certain parameter values. We show that our test is consistent for such alternatives also.
ISSN:0378-3758
1873-1171
DOI:10.1016/S0378-3758(99)00022-1