%0 Journal Article
%T Bayesian and Non-Bayesian Inference for Survival Data Using Generalised Exponential Distribution
%A Chris Bambey Guure
%A Samuel Bosomprah
%J Journal of Probability and Statistics
%D 2013
%I Hindawi Publishing Corporation
%R 10.1155/2013/364705
%X A two-parameter lifetime distribution was introduced by Kundu and Gupta known as generalised exponential distribution. This distribution has been touted to be an alternative to the well-known 2-parameter Weibull and gamma distributions. We seek to determine the parameters and the survival function of this distribution. The survival function determines the probability that a unit under investigation will survive beyond a certain specified time, say, ( ). We have employed different data sets to estimate the parameters and see how well the distribution can be used to analyse survival data. A comparison is made about the estimators used in this study. Standard errors of the estimators are determined and used for the comparisons. A simulation study is also carried out, and the mean squared errors and absolute bias are obtained for the purpose of comparison. 1. Introduction As the need grows for conceptualization, formalization, and abstraction in biology, so too does mathematics¡¯ relevance to the field according to Fagerstr£¿m et al. [1]. Mathematics is particularly important for analysing and characterizing random variation, for example, size and weight of individuals in populations, their sensitivity to chemicals, and time-to-event cases, such as the amount of time an individual needs to recover from illness. The frequency distribution of such data is a major factor determining the type of statistical analysis that can be validly carried out on any data set. Many widely used statistical methods, such as ANOVA (analysis of variance) and regression analysis, require that the data be normally distributed, but only rarely is the frequency distribution of data tested when these techniques are used (Limpert et al.) [2]. Gupta and Kundu [3] recently proposed the two-parameter generalised exponential distribution as an alternative to the lognormal, gamma, and Weibull distributions and did some studies on its properties. Some references on distribution are Raqab [4], Raqab and Ahsanullah [5], Zheng [6], and Kundu and Gupta [7]. According to Gupta and Kundu [8], the two-parameter can have increasing and decreasing failure rates depending on the shape parameter. Some research has been done to compare MLE to that of the Bayesian approach in estimating the survival function and the parameters of the Weibull distribution which are similar to the generalised exponential distribution. Amongst others, Sinha [9] determined the Bayes estimates of the reliability function and the hazard rate of the Weibull failure time distribution by employing only squared error loss
%U http://www.hindawi.com/journals/jps/2013/364705/