The Bivariate Length Biased - Power Garima Distribution Derived from Copula: Properties and Application to Environmental Data
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Abstract
Bivariate distributions calculate the probabilities for simultaneous outcomes of two random variables. They are essential for understanding the relationship between two variables. This study proposed a new bivariate distribution called the bivariate length biased power Garima (BLBPG) distribution, created by combining the Farlie-Gumbel-Morgenstern (FGM) copula with a length-biased power Garima distribution. The BLBPG distribution describes lifetime bivariate data with a weak correlation between variables as a flexible alternative to bivariate lifetime distributions for modeling real-valued data in applications. The proposed distribution yielded various properties including joint conditional probability functions, reliability (survival) and hazard functions, and generating a random variable. The maximum likelihood estimation was presented to estimate the parameters of the proposed distribution and a Monte Carlo simulation study was conducted to evaluate the performance of the estimators. A practical application of the proposed bivariate distribution to analyze environmental data was also demonstrated.
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