Binomial-discrete Erlang-truncated exponential mixture and its application in Cancer Disease

Abstract

Abstract The probability mass function of Binomial-discrete Erlang-truncated exponential distribution, a mixture of binomial distributions with the number of trials (parameter n) taken after a discrete Erlang-truncated exponential distribution, is demonstrated in this paper by utilizing the probability generating function method. A comprehensive mathematical treatment of the proposed distribution and expressions of its density, cumulative distribution function, survival function, failure rate function, Quantile function, moment generating function, Shannon entropy, order statistics, and stress-strength reliability, are provided. The model's parameters are estimated using the maximum likelihood method. Two real-world lifetime count data sets from the cancer disease, both of which are right-skewed and over-dispersed, are fitted using the proposed BDETE distribution to evaluate its efficacy and viability. We expect the findings to become standard works in probability theory and its related fields.