one-way analysis of covariance is a popular and common statisticalmethod, wherein the equality of the means of several random variables whichhave a linear relationship with a random mathematical variable, is tested. inthis study, a method is presented to improve the one-way analysis of covari-ance when there is an uncertainty in accepting the statistical hypotheses. themethod deals with a fuzzy...

Propagating possibilistic and probabilistic variables through a mapping yields a fuzzy random variable. We propose a method to attach probability intervals to events pertaining to the output variable. We show that this method is consistent with classical approaches to fuzzy random variables and that the obtained probability interval is the mean value of the fuzzy probability defined by viewing ...

There are various types of uncertainty in the real world. This is a motivation to investigate the behavior of uncertain phenomena. Random phenomena is one class of objective uncertain phenomena which has been well studied. Probability theory is an efficient tool to study the behavior of random phenomena. Besides randomness, fuzziness is a basic type of subjective uncertainty initiated by Zadeh....

Fuzziness plays an essential role in the real world. Fuzzy set theory has been developed very fast since it was introduced by Zadeh (1965) [1]. A fuzzy set was characterized with its membership function by Zadeh. The term fuzzy variable was fist introduced by Kaufmann (1975) [2], and then appeared in Zadeh (1978) [3] and Nahmias (1978) [4] as a fuzzy set of real numbers. In order to establish t...

Fuzzy random variables possess several interpretations. Historically, they were proposed either as a tool for handling linguistic label information in statistics or to represent uncertainty about classical random variables. Accordingly, there are two different approaches to the definition of the variance of a fuzzy random variable. In the first one, the variance of the fuzzy random variable is ...

Abstract. In this paper, a family of skew-slash distributions is defined and investigated. We define the new family by the scale mixture of a skew-elliptically distributed random variable with the power of a uniform random variable. This family of distributions contains slash-elliptical and skew-slash distributions. We obtain the moments and some distributional properties of the new family of d...

in statistical inference, the point estimation problem is very crucial and has a wide range of applications. when, we deal with some concepts such as random variables, the parameters of interest and estimates may be reported/observed as imprecise. therefore, the theory of fuzzy sets plays an important role in formulating such situations. in this paper, we rst recall the crisp uniformly minimum ...

Rough random theory, generally applied to statistics, decision-making, and so on, is an extension of rough set theory and probability theory, in which a rough random variable is described as a random variable taking “rough variable” values. In order to extend and enrich the research area of rough random theory, in this paper, the well-known probabilistic inequalities (Markov inequality, Chebysh...

Conditional expectations are not commonly used outside of probability and statistics. We present here a short introduction and list of their properties. For a random variable Z and a random vector X, the conditional expectation E[Z|X] is itself a random variable because it is a function of the random variables in X. For continuous random variables, E[Z|X] is defined as E[Z|X = x] = ∫ dz z p(z|x...