Mehdi Shams

University of Kashan · Department of Statistics and Applications

In this paper, a method is proposed for testing statistical hypotheses about the fuzzy parameter of the underlying parametric population. In this approach, using definition of fuzzy random variables, the concept of the power of test and p value is extended to the fuzzy power and fuzzy p value. To do this, the concepts of fuzzy p value have been def...

This paper deals with proposing two family of similarity measures between Hesitant Fuzzy Linguistic Term Sets. It will proved that the proposed similar measures satisfy the properties of the axiomatic definition for similarity measures and introduces several theorems. A method is also suggested to rank Hesitant Fuzzy Linguistic Term Sets. Then some...

This article modifies evaluating the probability of a fuzzy event based on a classical probability space introduced by Yager (Inform. Sci. 1979;18:113–122). The presented theoretical results will be illustrated with some propositions and remarks. It is shown that a modification in the definition of fuzzy probability of fuzzy events into a concept o...

In this paper, we consider sufficiency of the pair \((t,\pi )\) where \(\pi \) is a canonical projection which is maximal invariant and t is a maximum likelihood estimator which is weakly equivariant. We define weak structural sufficiency for \((t,\pi )\) and then we will consider the conditions under which \((t,\pi )\) is weakly structurally suffi...

In this paper, we shall generalize the concept of equivariance in statistics to “weak equivariance”. Then, we summarize the properties of weakly equivariant estimators and their applications in statistics. At first we characterize the class of all weakly equivariant estimators. Then, we shall consider the concept of cocycles and isovariance, and so...

This paper proposed an extension for the classical partial univariate regression model with non-fuzzy inputs and triangular fuzzy output. For this purpose, the popular non-parametric estimator and the conventional arithmetic operations of triangular fuzzy numbers were combined to construct a fuzzy univariate regression model. Then, a hybrid algorit...

This paper extends the sign test to the case where data are observations of fuzzy random variables, and the hypotheses are imprecise rather than crisp. In this approach, first a new notion of fuzzy random variables is introduced. Then, the alpha-level sets of the imprecise observations are transacted to extend the usual method of sign test. To do t...

In this paper, by using a Cramer - Rao inequality we obtained a lower bound minimax risk based on a random sample of random stopping time, in a condition of the truncated parameter space. Finally, as applications, we obtained minimax estimators under censored data, Koziol - Green model and exponential distribution family.

Based on a given Bayesian model of multivariate normal with known variance matrix we will find an empirical Bayes confidence interval for the mean vector components which have normal distribution. We will find this empirical Bayes confidence interval as a conditional form on ancillary statistic. In both cases (i.e. conditional and unconditional emp...

Equivariant functions can be useful for constructing of maximal invariant statistic. In this article, we discuss construction of maximal invariants based on a given weakly equivariant function under some additional conditions. The theory easily extends to the case of two or more weakly equivariant functions. Also, we derive a maximal invariant stat...