¹Shahid Chamran University of Ahvaz, Faculty of Mathematical Sciences and Computer, Department of Statistics, Ahvaz, Iran. PhD Student. Email: a-pak@scu.ac.ir
²Shahid Chamran University of Ahvaz, Faculty of Mathematical Sciences and Computer, Department of Statistics, Ahvaz, Iran. Associate professor. Email: parham-g@scu.ac.ir
³Shahid Chamran University of Ahvaz, Faculty of Mathematical Sciences and Computer, Department of Mathematics, Ahvaz, Iran. Associate professor. Email: seraj.a@scu.ac.ir

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.

Key words: Bayesian estimation, EM algorithm, Fuzzy data analysis, Maximum likelihood principle.

Los procedimientos clásicos de estimación para los parámetros de la distribución Weibull se encuentran basados en datos precisos. Se asume usualmente que los datos observados son números reales precisos. Sin embargo, algunos datos recolectados podrían ser imprecisos y ser representados en la forma de números difusos. Por lo tanto, es necesario generalizar los métodos de estimación estadísticos clásicos de números reales a números difusos. En este artículo, diferentes métodos de estimación son discutidos para los parámetros de la distribución Weibull cuando los datos disponibles están en la forma de números difusos. Estos incluyen la estimación por máxima verosimilitud, la estimación Bayesiana y el método de momentos. Los procedimientos de estimación se discuten en detalle y se comparan vía simulaciones de Monte Carlo en términos de sesgos promedios y errores cuadráticos medios.

Palabras clave: algoritmo EM, análisis de datos difusos, estimación Bayesiana, principio de máxima verosimilitud.

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