Title: Bayesian prediction of unobserved values for Type-II censored data for an inverse Weibull distribution
Authors: Takeshi Kurosawa - Tokyo University of Science (Japan) [presenting]
Tatsuya Kubota - Tokyo University of Science (Japan)
Abstract: Censoring problems often arise in survival time analysis. In survival time analysis, a Weibull distribution and an inverse Weibull distribution are often used. Hence, we focus on Type-II censored data for the inverse Weibull distribution. The aim is to derive posterior predictive distributions of unobserved values for Type-II censored data. These functions are given by integrals of conditional density functions and conditional survival functions over two hyper parameters. The conditional survival functions were also expressed by integral forms in previous studies. The integrals of the conditional survival functions are calculated by Monte Carlo integrations and it takes too much time to compute. Therefore, we derive the conditional survival functions in closed forms using a theory of order statistics and thereby reduce the computation cost. In addition, we calculate the predictive confidence intervals of unobserved values, coverage probabilities of unobserved values by using the derived posterior predictive survival functions and confirm the correctness of our derived functions.