On the negatively mixed distributions and their properties

A density (mass) function of negatively mixed distributions can be derived from the mixture of density (mass) function with negative weights. This article constructs the negatively mixed distribution and derives its properties, including the cumulative distribution function, raw moments, and moment generating and characteristic functions. Furthermore, we provide the notion of Negatively Mixed Exponential distribution and investigate its properties. We also propose the parameter estimation based on the method of moments and the maximum likelihood methods. The performance of estimators has been performed through the Monte Carlo simulation study. Moreover, the dataset has been analyzed to show how the proposed model and method work in practice.