Bayesian inference and life testing plans for generalized exponential distribution

Abstract

Recently generalized exponential distribution has received considerable attentions. In this paper, we deal with the Bayesian inference of the unknown parameters of the progressively censored generalized exponential distribution. It is assumed that the scale and the shape parameters have independent gamma priors. The Bayes estimates of the unknown parameters can not be obtained in closed form. Lindley's approximation and importance sampling technique have been suggested to compute the approximate Bayes estimates. Markov Chain Monte Carlo method has been used to compute the approximate Bayes estimates and also to construct the highest posterior density credible intervals. We also provide different criteria to compare two different sampling schemes and hence to find the optimal sampling schemes. It is observed that finding the optimum censoring procedure is a computationally expensive process, and we have recommended to use the sub-optimal censoring procedure, which can be obtained very easily. Monte Carlo simulations are performed to compare the performances of the different methods and one data analysis has been performed for illustrative purposes.

Bayesian Two-sample Prediction with Progressively Censored Data for Generalized Exponential Distribution Under Symmetric and Asymmetric Loss Functions

“…Case I: α and λ have independent gamma prior distributions Assume that α and λ are independent and follow the gamma (informative) prior densities (see, Kundu and Pradhan (2009b)) as…”

“…If both parameters are unknown, the joint conjugate priors do not exist. But because of flexibility of gamma distributions which includes the Jeffreys (non-informative) prior as a special case, we suggest the independent gamma priors on the scale and shape parameters (see also, Kundu and Pradhan (2009b)). For Bayesian analysis of the gamma distribution, Son and Oh (2006) assumed the gamma prior on the scale parameter and independent non-informative prior on the shape parameter, which is a special case of the gamma distribution.…”

Reliability sampling plans for a lognormal distribution under progressive first-failure censoring with cost constraint

“…. , n − m), (see Kundu and Pradhan 2009). Here n denotes the number of groups and m depends upon the degree of censoring λ which is equal to [n(1 − λ)], where [s] denotes the greatest integer less than or equal to s. Furthermore, when the optimal censoring does not lie on the extreme points on the convex hull, those cases are reported in the Table 2.…”

An Extended Exponentiated Exponential Distribution and its Properties

“…Many authors derived other properties of the (EE) distribution, Gupta and Kundu [7], Raqab [16], Zheng [22], Shirke et al [18],9 Abdel-Hamid and Al-Hussaini [1], Kundu and Pradhan [10] and Aslam et al [4]. Some generalizations of the EE distribution are discussed in Nadarajah and Kotz [13].…”