On a Class of Random Variables

On a Class of Random Variables

where f(rea) =f(z) is any analytic function regular in a circle of radius R>r about the origin. We can define a particular complex valued random variable Z in the following way: \Z\ =r with probability one, and arg Z is uniformly distributed on the interval [— x, x]. We shall denote by E the linear operator which "takes the expected value" of Z and of measurable functions of Z with respect to t...

A Survey on Simulating Stable Random Variables

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)

On Inverse Moments for a Class of Nonnegative Random Variables

On the Ratio of Rice Random Variables

 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...

A Probability Space based on Interval Random Variables

This paper considers an extension of probability space based on interval random variables. In this approach, first, a notion of interval random variable is introduced. Then, based on a family of continuous distribution functions with interval parameters, a concept of probability space of an interval random variable is proposed. Then, the mean and variance of an interval random variable are intr...