Construction of a New Bivariate Mixture Lindley Power Function Distribution with Functional Shape Parameter Utilizing Non-Identical Distributions via Conditional Approach

This paper presents a new bivariate mixture Lindley power function (BMLPF) distribution that employs a conditional approach with non-identical asymmetric distributions, distinguishing itself by the incorporation of a functional shape parameter. Various structural properties of bivariate distribution are presented, including explicit marginals, cumulative distribution function (CDF), product moments, correlation coefficients, conditional densities, moment generating functions, conditional mean, and variances. The parameters of the proposed distribution are evaluated using the maximum likelihood estimation method. To assess the effectiveness of this estimation approach, an extensive simulation study is carried out. The analysis quantifies these point estimators with their standard errors, RMSE, LCL, and UCL. This research significantly contributes to the development and application of bivariate distributions particularly in modeling and analyzing various types of data.