Estimating the Risk Function Using the Log-Logistic Regression Model for Environmental Pollution Data

Abstract

Log-Logistic distribution contains a non-linear risk function (non-monotonous), it can be used to model some survival data sets and shield them from the risks associated with environmental pollution in the modern era, which led to the spread of various diseases, such as cancer, hyperactivity, breathing issues, and other diseases, that have become prevalent in our society. A Log-Logistic regression model has been described in which the risk function of each sample that relates to time and also provides a linear model of survival probability at any specified time. In this research, the risk function of the Log-Logistic regression model was estimated using the maximum likelihood approach and the genetic algorithm method in the presence of generalized order statistics. These techniques were applied to air pollution data obtained from the Central Refineries Company in Baghdad (Al-Dora Refinery) daily environmental pollution compounds, which are based on time for the years 2018 to 2020.