Inference for exponential parameter under progressive Type-II censoring from imprecise lifetime

Abstract

Progressively Type-II censored sampling is an important method of
obtaining data in lifetime studies. Statistical analysis of
lifetime distributions under this censoring scheme is based on
precise lifetime data. However, in real
situations all observations and measurements of progressive Type-II censoring scheme are not precise numbers but more or less non-precise, also called fuzzy. In this paper, we consider the estimation of exponential mean
parameter under progressive Type-II censoring scheme, when the
lifetime observations are fuzzy and are assumed to be related to
underlying crisp realization of a random sample. We propose a new
method to determine the maximum likelihood estimate (MLE) of the
unknown mean parameter. In addition, a new numerical method for
parameter estimation based on fuzzy data is provided. Using the parametric bootstrap
method, we then discuss the construction of confidence intervals
for the mean parameter. Monte Carlo simulations are performed to
investigate the performance of all the different proposed
methods. Finally, an illustrative example is also included.