Fuzzy statistics and random variables represent a progressive fusion of traditional probability theory with the principles of fuzzy logic, enabling the treatment of imprecision and vagueness inherent ...

\item We use a capital letter, like $X$, to denote a random variable \item The values of a random variable are denoted with a lowercase letter, in this case $x$ \item ...

Abstract: In this chapter, we introduce the concept of a random variable and develop the procedures for characterizing random variables, including the cumulative distribution function, as well as the ...

This note suggests that expressing a distribution function as a mixture of suitably chosen distribution functions leads to improved methods for generating random variables in a computer. The idea is ...

Abstract: In this chapter, we first introduce the joint statistical behavior of multiple random variables, and then the focus turns toward the marginal and conditional cdfs, pdfs, and pmfs. In the ...

In this paper, we extend Stein’s method to products of independent beta, gamma, generalised gamma and mean zero normal random variables. In particular, we obtain Stein operators for mixed products of ...

ABSTRACT: This in virtue of the notion of likelihood ratio and the tool of moment generating function, the limit properties of the sequences of random discrete random variables are studied, and a ...

ABSTRACT: In this paper, we obtain the strong law of large numbers for a 2-dimensional array of pairwise negatively dependent random variables which are not required to be identically distributed. We ...