Bayes statistical decisions with random fuzzy data – an application for the Weibull distribution

Testing statistical hypotheses is one of the most important parts of statistical inference. On the other hand it can be regarded as a part of the decision theory. In the decision theory we assume that decisions (actions belonging to a certain action space) should depend upon a certain state which is uncontrollable and unknown for a decision maker. We usually assume that unknown states are generated by random mechanisms. However, all we could know about these mechanisms

[1]  Mark P. Kaminskiy,et al.  A simple procedure for Bayesian estimation of the Weibull distribution , 2005, IEEE Transactions on Reliability.

[2]  Pedro Gil,et al.  On the use of Zadeh's probabilistic definition for testing statistical hypotheses from fuzzy information , 1986 .

[3]  María Angeles Gil,et al.  Fundamentals and Bayesian analyses of decision problems with fuzzy-valued utilities , 1996, Int. J. Approx. Reason..

[4]  Huibert Kwakernaak,et al.  Fuzzy random variables--II. Algorithms and examples for the discrete case , 1979, Inf. Sci..

[5]  H. Carter.  Fuzzy Sets and Systems — Theory and Applications , 1982 .

[6]  Arturo J. Fernández.  Weibull inference using trimmed samples and prior information , 2009 .

[7]  Pedro Gil,et al.  The fuzzy decision problem: An approach to the problem of testing statistical hypotheses with fuzzy information , 1986 .

[8]  Reinhard Viertl,et al.  Statistical Methods for Fuzzy Data: Viertl/Statistical Methods for Fuzzy Data , 2011 .

[9]  Gordon Johnston,et al.  Statistical Models and Methods for Lifetime Data , 2003, Technometrics.

[10]  M. Casals,et al.  Bayesian testing of fuzzy parametric hypotheses from fuzzy information , 1993 .

[11]  Vincenzo Cutello,et al.  An Extension of the Axioms of Utility Theory Based on Fuzzy Rationality Measures , 2000 .

[12]  Olgierd Hryniewicz.  Estimation of Life-Time with Fuzzy Prior Information: Application in Reliability , 1988 .

[13]  Rudolf Kruse.  The strong law of large numbers for fuzzy random variables , 1982, Inf. Sci..

[14]  H. Raiffa,et al.  Applied Statistical Decision Theory. , 1961 .

[15]  Olgierd Hryniewicz,et al.  Soft Methods in Hypotheses Testing , 2001 .

[16]  L. Zadeh.  Fuzzy sets as a basis for a theory of possibility , 1999 .

[17]  Huibert Kwakernaak,et al.  Fuzzy random variables - I. definitions and theorems , 1978, Inf. Sci..

[18]  Olgierd Hryniewicz,et al.  Statistics with Imprecise Data , 2009, Encyclopedia of Complexity and Systems Science.

[19]  R. Schafer.  Bayesian Reliability Analysis , 1983 .

[20]  David Lindley,et al.  Optimal Statistical Decisions , 1971 .

[21]  Sylvia Frühwirth-Schnatter,et al.  On fuzzy Bayesian inference , 1993 .

[22]  Reinhard Viertl,et al.  Generalized Bayes’ theorem for non-precise a-priori distribution , 2004 .

[23]  Seyed Mahmoud Taheri,et al.  A Bayesian approach to fuzzy hypotheses testing , 2001, Fuzzy Sets Syst..

[24]  Olgierd Hryniewicz,et al.  Possibilistic Approach to the Bayes Statistical Decisions , 2002 .

[25]  Didier Dubois,et al.  Ranking fuzzy numbers in the setting of possibility theory , 1983, Inf. Sci..

[26]  R. Kruse,et al.  Statistics with vague data , 1987 .

[27]  Olgierd Hryniewicz,et al.  Fuzzy Sets in the Evaluation of Reliability , 2007, Intelligence in Reliability Engineering.

[28]  R. Viertl.  Statistical Methods for Fuzzy Data , 2011 .