Bivariate Geometric Model

Abstract

Geometric distribution is a very useful probability distribution in addressing some important aspects of real-life data. As the geometric distribution addresses the first time occurrence of an event after successive failures, it may be employed to explore the characteristics of incidence of a disease, recovery from a disease, failure of a product first time after providing service without failure successively at discrete time points, etc. In other words, geometric distribution can be considered as a discrete counterpart of exponential distribution which plays a very important role for analyzing survival or reliability data. In many occasions, we need to examine the incidence from competing risk point of view when both the outcome variables are correlated. In health data, often there are occurrences of two correlated outcomes for the first time or incidence of two symptoms, diseases, or conditions. The repeated measures data on the outcomes at different times observed longitudinally provide us with the scope for modelling correlated outcomes as functions of potential risk factors. For example, there may be association between incidence of diabetes and heart diseases but due to absence of a suitable technique, it would be difficult to understand the underlying mechanism properly. A bivariate geometric model can provide insights to examine such relationships.