Generalized Estimation for Two-Parameter Life Time Distributions Based on Fuzzy Life Times

Abstract

Ongoing developments of the measurement sciences say that measurements based on continuous phenomena are no more precise observations but more or less fuzzy. Therefore, it is necessary to utilize this imprecision of observations to obtain such estimators, which are based on all the available information that is given in the form of randomness and fuzziness. Objective of this research was to get such parameter estimation procedure that utilizes all the available information for some well-known two-parameter life time distributions. Therefore, the estimators need to be generalized in such a way to cover both uncertainties. For this purpose, based on $\delta$ -cuts of the life time observations, the generalized estimators are developed in such manner to cover stochastic variation in addition to fuzziness. The proposed generalized estimators are much preferred over classical estimators for life time analysis as these are based on all the available information present in the form of fuzziness of single observations and random variation among the observations to make suitable inferences.