Estimation for a Regression Model Based on Log Generalized Inverse Generalized Weibull Distribution under Type I Censoring

Abstract

The Log Generalized Inverse Generalized Weibull (LGIGW) distribution, obtained by taking the logarithm of a Generalized Inverse Generalized Weibull (GIGW) random variable, is introduced and studied in this work. The proposed distribution is particularly useful for modeling lifetime, financial, and reliability data due to its flexibility in capturing various data behaviours. It encompasses several well-known classical distributions as special cases. In addition, a corresponding regression model based on the LGIGW distribution is developed. This model generalizes a number of existing regression models available in the literature, which arise as special cases under specific parameter settings. Parameter estimation is carried out using the method of maximum likelihood, and the performance of the estimators is assessed through Monte Carlo simulation studies. The applicability of the proposed model is illustrated using two real-life data sets. Model comparison is conducted using standard information criteria, including the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and the corrected Akaike Information Criterion (AICc). Furthermore, sensitivity analysis and residual diagnostic techniques are employed to identify influential observations.