In this article, a new bivariate Poisson distribution, called the type-1 imbalanced bivariate Poisson distribution, is introduced for dependence modeling among the random number of visits made by a patient and the number of prescriptions written by a physician. By utilizing the proposed model, the article discovers patterns on the implications of the over-visits made by the patients. This new discrete bivariate Poisson probability mass function is quite interesting and useful to the healthcare researchers. Its statistical properties are derived. The concepts and methodology around its imbalance parameter,\( \phi \), are constructed and illustrated using the Australian Health Survey data for 1997–1998. The data analytic results in the illustration demystify the implications when the patients make more visits to the physician.
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The author sincerely appreciates and thanks a knowledgeable and much encouraging referee and the editor Dr. Sat Gupta for many valuable suggestions which enabled to improve the presentation and readability in the manuscript greatly.
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