Advancing Bayesian Inference: Fitting Type I Half-logistic Nadarajah-Haghighi Distribution and its Comparison with Related Distributions for Censored Survival Data

Abstract

In recent years, the field of Bayesian modeling of generalized distributions has garnered substantial attention. This surge in interest can be attributed to the remarkable strides made in computational capabilities and the enhanced accessibility of sophisticated software tools. This study aims to apply Bayesian inference methods to the Type I Half-logistic Nadarajah- Haghighi model and compares it with the Exponential model and the Type I Half-logistic Exponential model. These distributions are analyzed and fitted to censored survival data using the probabilistic programming language STAN. To incorporate censored mechanisms within the STAN framework, customized codes are developed. The models are then compared using fully Bayesian model selection methods.. KEYWORDS :Censored data, Nadarajah-Haghighi distribution, Type I half-logistic family, LOOIC, WAIC, STAN.