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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the notion of a $d$-poset was introduced in a connection withquantum mechanical models. in this paper, we introduce theconditional expectation of  random variables on thek^{o}pka's $d$-poset and prove the basic properties ofconditional expectation on this  structure.

A general approximation formula for the moment-generating function of random variables with broadly distributed logarithms is derived using a saddle-point expansion of the defining integral. As a special case, a simple and accurate approximation formula for the momentgenerating function of log-normal distributions is obtained. For 4.3 dB spread it reaches 0.5% accuracy and improves rapidly as t...

Metatimes constitute an extension of time-change to general measurable spaces, defined as mappings between two σ-algebras. Equipping the image σ-algebra a metatime with measure and defining composition given by on domain σ-algebra, we identify metatimes bounded linear operators spaces square integrable functions. We also analyse possibility define from operator Hilbert which show is possible fo...