Abstract
The Topp-Leone distribution was introduced by Topp-Leone in 1955. In this paper, an attempt has been made to fit Topp-Leone Generalized Exponential distribution. Since, Topp-Leone distribution contains only one parameter and its support set is restricted to (0,1), because of this, in most practical situations it is not a better fit for the lifetime modelling. So an extension of this distribution is required. A Bayesian approach has been adopted to fit this model as survival model. A real survival data set is used to illustrate. Implementation is done using R and JAGS and appropriate illustrations are made. R and JAGS codes have been provided to implement censoring mechanism using both optimization and simulation tools.
Highlights
Topp-Leone (1955) constructed the distribution for empirical data with J-shaped histogram such as powered band tool failures, and automatic calculating machine failure
Bayesian Analysis of Topp-Leone Generalized Exponential distribution (TLGE) Distribution results analytically and the function LaplacesDemon simulates the results from the posterior density with one of the several Metropolis algorithms Markov Chain Monte Carlo (MCMC)
Many simple Bayesian analyses based on noninformative prior distribution give similar results to standard non-Bayesian approaches, for example, the posterior t-interval for the normal mean with unknown variance
Summary
Topp-Leone (1955) constructed the distribution for empirical data with J-shaped histogram such as powered band tool failures, and automatic calculating machine failure. For the purpose of Bayesian analysis of this model, two important techniques, one is asymptotic approximation and the other is simulation methods, are implemented using LaplacesDemon and R2jags packages of R. Bayesian Analysis of TLGE Distribution results analytically and the function LaplacesDemon simulates the results from the posterior density with one of the several Metropolis algorithms Markov Chain Monte Carlo (MCMC). Another function is JAGS (Just Another Gibbs Sampler).
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