Analytical and Computational Studies for the Two‐Parameter Exponential Mixture Model

ABSTRACT Finite mixture models are frequently employed to model heterogeneous populations and capture multi‐modality. The present literature has extensively studied numerous parametric forms but not explored finite mixtures of two‐parameter exponential distributions. In this article, we have considered a mixture of two two‐parameter exponential distributions and proved the identifiability. We have derived estimators for the location, rate, and mixing proportion parameters using the classical Expectation Conditional Maximization algorithm and Bayesian methods based on conjugate priors for the rate and mixing proportions. To evaluate the performance of these proposed estimators, Monte Carlo simulations are conducted across varying sample sizes, mixing proportions, and degrees of component overlap, with mean squared error (MSE) and bias as the performance criteria. The simulation results indicate that the Bayesian estimators outperform the maximum likelihood estimators in terms of MSE as well as bias across most of the parameter space. Finally, the applicability of the proposed model and estimation procedures is illustrated through a real‐life dataset.