Estimating the survival function of people infected with covid-19 in the holy city of Karbala by a proposed new probability model

Abstract

This research presented the mixed probabilistic model ( Frecht - Gamma), which was obtained by mixing two single distributions, namely the Gamma(2,β) distribution, and the Frecht distribution, using a parameter known as the parameter mixing between the distributions (α) in order to obtain a new probability distribution characterized by accuracy. comprehensiveness, modernity, and flexibility in representing the data of the phenomenon studied, and the research mainly aims to estimate the survival function by using amethod for the Maximum Likelihood Method and Moment, but on the experimental side, Monte Carlo simulations were employed by the rejection and acceptance method to generate random data for a sample. It consists of three sample sizes (25,50,100) that follow the mixed model (Frecht - Gama) in order to give a complete idea of the statistical measures used and by using the statistical indicator, the mean integral error squares (IMSE) to compare the preference of the estimation methods used. It showed the preference of the Maximum Likelihood Method (ML) in estimating the survival function for medium and large sample sizes. The empirical and applied sides: Confirming the use of the greatest possibility method to estimate the survival function at medium and large sample sizes, as well as recommending the adoption of the research results at the Holy Karbala Health Department.