Estimating the survival function using the bivariate Weibull distribution based on the coupling function (IFM) with application

Abstract

     In analyzing a bivariate survival function, estimating the joint distribution function and measuring the relationship and correlation between survival times is of great importance, since the existence of this correlation, even if weak, will affect the estimates of the distribution function and thus be the influencing factor in the survival function. Therefore, coupling functions are commonly used to estimate multivariable distributions based on marginal. The research aims to study the characteristics of the bivariate Weibull distribution based on the function (FGM), and to estimate the parameters of this distribution.

     Two methods for estimating the parameters of bivariate Weibull distribution were also presented. These are the Maximum likelihood (ML) method and the Inference Functions for Marginal Distributions (IFM) method

     The Simulation method was used to investigate the best method for estimating the distribution parameters. It was found that the best method is the (ML) method. The study was then applied to real data representing the times to the first and second recurrences of infection at the catheter insertion point in kidney patients undergoing dialysis.