Stochastic Modelling on New Mixture Distribution with Properties and Their Application

In this article, the authors propose a new two-parameter continuous distribution. It is called a new mixture distribution because it comes from the unique combination of exponential and gamma distributions (MEGD). Some statistical properties of the distribution are derived, such as the moments, moments generating function, reliability analysis. Also, the distribution of order statistics is presented, and entropies are derived. The application of the maximum likelihood estimation technique to the performance of traditional parameter estimates. Two authentic data sets describing cancer patients' survival are used to empirically demonstrate the potential importance and usability of the proposed distribution. Comparing the new mixture distribution to some other competing distribution, the analysis's results demonstrated that it performed quite well.