An extended Marshall-Olkin simulated Pareto-exponential distribution: development, properties and application

Abstract

Marshal-Olkin simulated Pareto-exponential distribution (MOSPED) is a new distribution developed from simulated Pareto-Exponential distribution (SPED) by using Marshal-Olkin technique. SPED is a special distribution which emerges out as a marginal distribution of Bivariate Affine-Linear Exponential (BALE) distribution by Mohsin et al. (2014) without adopting any procedure. Some mathematical properties of the proposed distribution including moments, mean variance, incomplete moments are discussed along with its characterization. The reliability analysis of MOSPED comprising survival function, hazard function, reversed hazard function along with different types of entropies such as Renyi entropy, β-entropy and γ-entropy are presented. We also develop and discuss the distributions of series as well as parallel systems for the proposed distribution to observe the performance of each component in the product. Moreover, we estimate the unknown parameters of our model, parallel system and series system by using the method of maximum likelihood estimation for each distribution. A simulation study is performed to observe the stability and consistency of the model parameters. The application of the MOSPED is presented by using three real life data sets and its comparison with some baseline distributions is given on the basis of log-likelihood, AIC and BIC.