Statistical Investigations of Sarmanov Bivariate Weibull Distribution with Application to Medical Data

The Weibull distribution is highly versatile and capable of fitting various shapes of datasets. It is similar to the normal distribution, which is a unimodal distribution that represents probabilities for continuous data. This distribution is often considered the most fundamental and elementary lifespan distribution. This work utilizes the Sarmanov copula and Weibull marginal distribution to construct a bivariate distribution known as the bivariate Weibull Sarmanov distribution (BW-SARD). The statistical characteristics of the BW-SARD are examined, including marginal distributions, product moment, moment generating function, coefficient of correlation between the inner variables, conditional distributions, and conditional expectation. In addition, we calculate various reliability measures, including the hazard rate function, reversed hazard rate function, positive quadrant dependence property, mean residual life function, and vitality function. Model parameter estimation is conducted using the maximum likelihood and Bayesian approaches. Ultimately, genuine data collection is presented, and examined to explore the model, and valuable outcomes are acquired for illustrative intentions