Annals of Data Science https://doi.org/10.1007/s40745-019-00228-1 Bayesian Survival Analysis of Type I General Exponential Distributions Mohammed H. AbuJarad 1 · Eman S. A. AbuJarad 2 · Athar Ali Khan 1 Received: 30 April 2019 / Revised: 22 June 2019 / Accepted: 13 July 2019 © Springer-Verlag GmbH Germany, part of Springer Nature 2019 Abstract This article aims at generalizing two distribution by means of, exponentiated exponen- tial and Weibull distribution. The researchers have employed three and four parameters life model called the Type I General Exponential exponentiated exponential distribu- tion and Type I General Exponential Weibull distribution. Survival and hazard rate functions were provided for these two models. To fit these models into survival and hazard rate functions, we adopted the Bayesian approach. For illustration, a real sur- vival data set has been employed. Application is carried out by R and Stan. Finally,a comparison between these two models is made by using loo package to find the best model and simulation. Keywords Posterior · Simulation · Loo · RStan · Bayesian Inference · WAIC · R · HMC 1 Introduction Hamedani et al. [1] constructed new generate extended families. they present a new class of distributions called the Type I General Exponential (TIGE) family of dis- tributions. In this paper, aim is to fit the Type I General Exponential exponentiated exponential distribution (TIGEEE) and Type I General Exponential Weibull distribu- tion (TIGEW) using a Bayesian approach and this distribution has an important role in lifetime modelling. Statistical methods for lifetimes data analysis have continued to B Mohammed H. AbuJarad m.jarad@gu.edu.ps Eman S. A. AbuJarad emanjarad2@gmail.com Athar Ali Khan atharkhan1962@gmail.com 1 Department of Statistics and Operations Research, AMU, Aligarh 202002, India 2 Department of Mathematics, AMU, Aligarh 202002, India 123