%0 Journal Article
%T Estimation of Parameters of Generalized Inverted Exponential Distribution for Progressive Type-II Censored Sample with Binomial Removals
%A Sanjay Kumar Singh
%A Umesh Singh
%A Manoj Kumar
%J Journal of Probability and Statistics
%D 2013
%I Hindawi Publishing Corporation
%R 10.1155/2013/183652
%X We obtained the maximum likelihood and Bayes estimators of the parameters of the generalized inverted exponential distribution in case of the progressive type-II censoring scheme with binomial removals. Bayesian estimation procedure has been discussed under the consideration of the square error and general entropy loss functions while the model parameters follow the gamma prior distributions. The performances of the maximum likelihood and Bayes estimators are compared in terms of their risks through the simulation study. Further, we have also derived the expression of the expected experiment time to get a progressively censored sample with binomial removals, consisting of specified number of observations from generalized inverted exponential distribution. An illustrative example based on a real data set has also been given. 1. Introduction The one parameter exponential distribution is the simplest and the most widely discussed distribution in the context of life testing. This distribution plays an important role in the development to the theory, that is, any new theory developed can be easily illustrated by the exponential distribution due its mathematical tractability; see Barlow and Proschan [1] and Leemis [2]. But its applicability is restricted to a constant hazard rate because hardly any item/system can be seen which has time independent hazard rate. Therefore, the number of generalizations of the exponential distribution has been proposed in earlier literature where the exponential distribution is not suitable to the real problem. For example, the gamma (sum of independent exponential variates) and Weibull (power transformed distribution) distributions are the most popular generalizations of the exponential distribution. Most of the generalizations of the exponential distribution possess the constant, nonincreasing, nondecreasing and bathtub hazard rates. But in practical real problems, there may be a situation where the data shows the inverted bathtub hazard rate (initially increases and then decreases, i.e., unimodal). Let us take an example, in the course of study of breast cancer data, we observed that the mortality increases initially, reaches to a peak after some time, and then declines slowly, that is, associated hazard rate is inverted bathtub or particularly unimodal. For such types of data, another extension of the exponential distribution has been proposed in statistical literature. That is known as one parameter inverse exponential or one parameter inverted exponential distribution (IED) which possess the inverted bathtub hazard rate.
%U http://www.hindawi.com/journals/jps/2013/183652/