Simulated Exact Confidence Intervals: With Applications to Censored Exponential Reliability Data

Abstract

A method for constructing exact simulated confidence intervals is presented, valid for situations with both discrete and continuous observations. The idea of the method is to invert a data generating function, which needs not be monotone, and where special attention is taken when the data generating function contains jumps. The method is applied to obtain exact confidence intervals for certain types of censored data from exponential distributions. The censoring schemes under study are earlier treated in the literature, and a comparison to these approaches is considered. The connection to fiducial inference is discussed, and a difference in the paradigm of obtaining intervals for the parameter is studied.