Advances in Discrete Lifetime Modeling: A Novel Discrete Weibull Mixture Distribution with Applications to Medical and Reliability Studies

In recent years, there has been growing interest in discrete probability distributions due to their ability to model the complex behavior of real-world count data. In this paper, a new discrete mixture distribution based on two Weibull components is introduced, constructed using the general discretization approach. Several important statistical properties of the proposed distribution, including the survival function, hazard rate function, alternative hazard rate function, moments, quantile function, and order statistics are derived. It was concluded from the descriptive measures that the discrete mixture of two Weibull distributions transitions from being positively skewed with heavy tails to a more symmetric and light-tailed form. This demonstrates the high flexibility of the discrete mixture of two Weibull distributions in capturing a wide range of shapes as its parameter values vary. Estimation of the parameters is performed via maximum likelihood under Type II censoring scheme. A simulation study assesses the performance of the maximum likelihood estimators. Furthermore, the applicability of the proposed distribution is demonstrated using two real-life datasets. In summary, this paper constructs the discrete mixture of two Weibull distributions, investigates its statistical characteristics, and estimates its parameters, demonstrating its flexibility and practical applicability. These results highlight its potential as a powerful tool for modeling complex discrete data.