Bayes Estimator of Survival Probability from Randomly Censored Observations with Weibull Distribution of Time to Death

Abstract

SummaryThis paper deals with Beyea estimation of survival probability when the data are randomly cenmred. such a situation arks in came of a clbkal trial which extends for 8 limited period T. A fixed number of patienta (n) are observed whose times to death have identical Weibull distribution with parameters B and 8. The maximum times of observation for different patients are also independent uniform variables as the patienta arrive randomly throughout the trial. For the joint prior dietribution of (/?. 8) as suggested by Snnu and UE (1980. page 137) Bayes estimator of survival probability a t time t (O<t< ! Z' ) hae been obtained. Considering squared error lcnre function it the mean of the survival probability with respect to the posterior distribution of (/?, 8). This estimator is then compared with the maximum likelihood estimator, by simulation, for various values of /?, 8 and censoring percentage. The proposed eatimator is found to be bettar under certain conditions.

Reliability estimation using doubly-censored field data

“…A uniform prior distribution has been chosen for B and a non-informative prior for 6. The joint prior is given by the product of two individual prior distributions Pandey (1987). usedSinha and Kale's (1980) result for the joint prior distribution of (B, 6) and obtained a Bayes estimator of reliability at time t (O<t<T).…”