Title: Estimation and prediction for a distribution with bathtub shape under progressive first failure censoring
Authors: Tanmay Kayal - Indian Institute of Technology Patna (India) [presenting]
Yogesh Mani Tripathi - Indian Institute of Technology Patna (India)
Abstract: A two-parameter distribution with bathtub shape under progressive first failure censoring is considered. We obtain maximum likelihood estimates of unknown parameters and then compute observed Fisher information matrix. Further we consider a non linear regression model to estimate the unknown parameters using least square estimation method and construct $95\%$ Bonferroni confidence intervals for the same. We also estimate the parameters using Bayesian approaches such as Tierney-Kadane method and Metropolis-Hastings algorithm against gamma prior distributions. One- and two-sample prediction problems are discussed under Bayesian framework. We study the performance of proposed methods using Monte Carlo Simulations and finally analyze a real data set for illustration purposes.