Goodness-of-fit tests for a Bi-Weibull competing risks model

Recently, the interest of researchers in creating statistical models has increased in the absence of critical values that play a fundamental role in the statistical analysis of the proposed model. In this paper, we are interested in proposing critical values for a very interesting model in the statistical literature. It is particularly useful when the data represents two distinct phases of risk, each of which can be modeled by a different Weibull distribution, called the bi-Weibull competing risks model. For this purpose, we employed the standard goodness-of-fit tests based on the empirical distribution functions (EDF) where determine the differences between the theoretical and empirical hypothesized distributions. We aim to build for different sample sizes, tables of critical values of Kolmogorov-Smirnov statistic, Anderson-Darling statistic, Cramer-Von Mises statistic, that's using the maximum likelihood estimation, Monte Carlo method with R software. The power of these statistics is studied using some alternatives such as the Bertholon competing risks distribution and the Weibull distribution.