The aim of this paper is to establish a theory of random variables on domains. Domain theory is a fundamental component of theoretical computer science, providing mathematical models of computational processes. Random variables are the mainstay of probability theory. Since computational models increasingly involve probabilistic aspects, it’s only natural to explore the relationship between thes...

Chance theory is put forward as a tool to deal with a complex system including randomness and uncertainty. As a fundamental concept in chance theory, uncertain random variable is an extension of random variable and uncertain variable. This paper obtains a new law of large numbers for independent uncertain random variables but not necessarily identically distributed.

The purpose of probability theory is to model random experiments so that we can draw inferences about them. The fundamental mathematical object is a triple (Ω,F , P ) called the probability space. A probability space is needed for each experiment or collection of experiments that we wish to describe mathematically. The ingredients of a probability space are a sample space Ω, a collection F of e...

Hoarding is characterized by the persistent difficulty discarding or parting with possessions, regardless of the value others may attribute to these possessions. Hoarding resembles obsessive compulsive disorder (OCD) in several ways. The avoidance of and difficulties with discarding seem to be driven by fears of losing something significant or being responsible for a bad outcome. These could be...

In general case, Chambers et al. (1976) introduced the following algorithm for simulating any stable random variables $ X/sim(alpha, beta, gamma, delta) $ with four parameters. They use a nonlinear transformation of two independent uniform random variables for simulating an stable random variable... (to continue, click here)

 The ratio of independent random variables arises in many applied problems. In this article, the distribution of the ratio X/Y is studied, when X and Y are independent Rice random variables. Ratios of such random variable have extensive applications in the analysis of noises of communication systems. The exact forms of probability density function (PDF), cumulative distribution function (CDF) a...

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We introduce the concept of an extremely negatively dependent (END) sequence of random variables with a given common marginal distribution. An END sequence has a partial sum which, subtracted by its mean, does not diverge as the number of random variables goes to infinity. We show that an END sequence always exists for any given marginal distributions with a finite mean and we provide a probabi...