A new family of bivariate alpha log power transformation model based on extreme shock models

This study presents a new bivariate distribution, referred to as the bivariate alpha log power transformation (BVALPT) model, developed by integrating the alpha log power transformation technique with the Marshall–Olkin extreme shock framework. Closed-form expressions for both the joint probability density function (pdf) and cumulative distribution function (cdf) are derived. The manuscript explores several key statistical properties of the proposed model, including marginal and conditional distributions, as well as survival and hazard rate functions. Parameter estimation is carried out using the maximum likelihood estimation (MLE) method. A notable special case, the bivariate alpha log power transformed exponential (BVALPTE) distribution, is examined in detail. The practical utility of the BVALPT family is demonstrated by fitting the BVALPTE distribution to a real-world dataset. Comparative results reveal that the BVALPTE offers an improved fit and enhanced analytical performance over the benchmark bivariate model considered in the analysis.