A Bayesian Estimation Procedure for One-Parameter Exponential Survival Distributions Facilitated by an Inverted Gamma Prior

A Bayesian estimation procedure for one-parameter exponential survival distributions facilitated by an inverted gamma prior was performed in this study using data obtained from data obtained from the University of Calabar Teaching Hospital (UCTH). The exponential survival distributions are just one amongst a number of distributions adopted for tackling problems in survival analysis, and may occur either in one parameter or two parameters under uncensored or censored conditions. The review of literature exposed the absence of studies addressing the need for an alternative procedure that carefully considered the peculiarities of the exponential survival distribution; hence, this study aimed to address this gap. Based on this, a Bayesian estimation technique was employed to estimate only the parameter of the one-parameter exponential survival distribution under uncensored and censored circumstances, with the survivorship and hazard functions deduced, thereafter. The results obtained showed that the parameter of the exponential survival distribution (λ) existed both for the one-parameter uncensored and censored cases of the exponential survival distribution, with known expressions. Both the MLE and Bayesian estimation results were simulated using real-life data, and the results showed near-convergence of the MLE and Bayesian estimation for unit values of the parameters of the inverted gamma prior used in the study.