On the Development of Fuzzy Estimators for Life Time Distributions

based on Censored Fuzzy Life Times

Mohammad Abiad 1 ∗ , Muhammad Shafiq 2 ∗, Syed Habib Shah2 , Muhammad Atif 3

1College of Business Administration, American University of the Middle East, Kuwait

2Institute of Numerical Sciences, Kohat University of Science & Technology, KP, Pakistan

3Department of Statistics, University of Peshawar, KP, Pakistan

Emails: mohammad.abiad@aum.edu.kw, shafiq@kust.edu.pk, shspk@yahoo.com, m.atif@uop.edu.pk.com

Abstract

Lifetime analyses comprise the techniques dealing with observations obtained from the occurrence of a specified

event(s). In most of the situations dealing with lifetime observations, some units are recorded as censored

observations. Dealing with censored observations makes these techniques unique. Countless standard statistical

tools are available for inference based on censored lifetime observations. These classical techniques

consider lifetime observations as precise numbers and ignore the uncertainty of single observations. Whereas

in practical applications it is not possible to measure life times as precise numbers, they are always more or less

nonprecise. The imprecision in measurements can be covered by neutrosophic set. Fuzzy estimators for life

time distributions potentially use neutrosophic system to model and analyze the inherent uncertainties and neutalities

present in the data and the parameter estimates. This study aimed to obtain estimators for the Weibull

parameters and two exponential parameters based on the up-to-date fuzzy number approach, a special case

for neutrosophic set. The suggested estimators incorporate fuzziness in addition to random variation, which

makes these estimators more realistic. The same techniques need to be extended to fuzzy and neutrosophic

sets.

Keywords: Characterizing function; Fuzzy numbers; Life time; Non-precise data; Neutrosophic sets