Development of New Flexible Lifetime Model: its Associated Inferences and Applications to Cancer and Covid-19 Data

Abstract

In this paper, a New Two-Parameter Generalized Lindley Distribution (NTGLD) for modelling lifetime data is proposed, which is designed to enhance the flexibility and applicability of the Lindley distribution in real data analysis. Key statistical properties such as the first four moments about the origin, coefficient of variation, hazard and survival functions of the NTGLD are equally obtained. The parameters of the NTGLD were estimated using the method of maximum likelihood. A comprehensive simulation study compares the efficiency of the estimators is presented. The quantile plot provides further insights, illustrating how the distribution's quantile varies with the parameters α and θ, emphasizing the adaptability of the model to different data structures. The NTGLD is applied to three real datasets: remission times of 128 bladder cancer patients, remission times of 36 bladder cancer patients, and recovery times of 553 Covid-19 patients. In each case, the NTGLD demonstrates superior fit compared to competing models considered in this study. Performance metrics such as Akaike Information Criteria, Akaike Information Criteria Corrected, Hannan–Quinn information criteria and Bayesian Information Criteria consistently favour the NTGLD, underscoring its robustness and effectiveness. This study establishes the NTGLD as a valuable tool for statistical modelling, offering significant improvements over existing distributions considered in terms of flexibility, accuracy, and fit.