On fitting the bi-Weibull competing risks distribution with application

Abstract

Survival analysis examines how long it takes an interesting event to occur. The lifespan of industrial systems, which are susceptible to various causes of failure, is described by competing risk models. Furthermore, when estimating the cause-specific mortality rate in the presence of other causes, mortality rate research took into account a variety of event types. One of the competing risks models that accurately describes this phenomenon is the bi-weibull distribution, which is the minimum between two Weibull distributions. In this work, after estimating the unknown parameters by several methods, we propose to construct a modified chi-square statistic to fit this model. This statistic can be used not only to recover information lost during data regrouping, but also to differentiate this distribution from its alternatives. A thorough simulation analysis and an application using actual data are provided to demonstrate the viability of the suggested test.