The Robust Linear Estimation of Logistic Distribution Parameters in Lifetime Data

Abstract

Outliers or non-normality in lifetime data can affect the accuracy of estimated parameters of mathematical distributions, including the logistic distribution. Therefore, robust estimators such as the rank regression method are often used to be less sensitive to outliers or non-normality. In this article, some robust estimation approaches are employed in rank regression estimation to be more robust to outliers. Proposed methods included the robust covariance between the transformed (dependent variable) and the original time values (independent variable) for the Fast Minimum Covariance Determinant method and robust linear regression for weight functions (Bi-square, Andrews, Cauchy, Fair, Huber, Logistic, Talwar, and Welsch) in estimation regression coefficients which can be employed in rank regression to estimate logistic distribution parameters. The efficiency of the traditional method (Rank Regression Method) and the proposed method was compared based on simulation data and real data representing the lifetime of Bacterial Toxemia children’s patients at Hefei Children’s Teaching Hospital. The study's results showed the efficiency of the proposed methods in handling outliers and the accuracy of estimating the parameters (Location and Scale) of the logistic distribution compared to the traditional method.