Inference for the Weibull Distribution Based on Fuzzy Data

Abstract

Classical estimation procedures for the parameters of Weibull distribution are based on precise data. It is usually assumed that observed data are precise real numbers. However, some collected data might be imprecise and are represented in the form of fuzzy numbers. Thus, it is necessary to generalize classical statistical estimation methods for real numbers to fuzzy numbers. In this paper, different methods of estimation are discussed for the parameters of Weibull distribution when the available data are in the form of fuzzy numbers. They include the maximum likelihood estimation, Bayesian estimation and method of moments. The estimation procedures are discussed in details and compared via Monte Carlo simulations in terms of their average biases and mean squared errors. Finally, a real data set taken from a light emitting diodes manufacturing process is investigated to illustrate the applicability of the proposed methods.

Keywords

• algoritmo EM
• análisis de datos difusos
• estimación Bayesiana
• principio de máxima verosimilitud