Affiliations: [a] Department of Information Systems and Business Analytics, Eastern Washington University, Cheney, WA, USA | [b] Department of Finance and Management Science, Washington State University, Pullman, WA, USA | [c] Department of Mathematics and Statistics, Washington State University, Pullman, WA, USA | [d] Department of Food, Land and Agribusiness Management, Harper Adams University, Newport, UK
Correspondence:
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Corresponding author: Alex Paparas, Department of Information Systems and Business Analytics, Eastern Washington University, 601 E. Riverside Ave, 99202, Cheney, WA, USA. Tel.: +1 509 339 9198; E-mail: apaparas@ewu.edu.
Abstract: In this study we develop a change point methodology to identify and estimate changes in the parameter of a Poisson distribution. The proposed methodology considers the case when the Poisson parameter changes abruptly at an unknown point of time. For this case, the maximum likelihood estimate of the change point and its asymptotic distribution are pursued. Mainly, we carry out a large scale simulation study for evaluating the appropriateness of the asymptotic distribution of the mle from the view point of finite samples, and also for evaluating the closeness under known and unknown parameters. The simulations study also compares the mle with that of a Bayesian estimate. Then, the methodology is applied to three examples. First, we uncover changes in the number of homicides in California using monthly data from January 2002 until December 2020. Secondly, data about deaths of females caused by stomach cancer is considered to detect possible changes in the numbers recorded from 1930 to 2011. Thirdly, British coal mining disasters from 1851 to 1962 in which more than 10 men were killed are analyzed.
Keywords: Change point estimation, detection, two-sided random walk, total variation distance, Poisson distribution, maximum likelihood estimate
