The sum of correlated gamma random variables appears in the analysis of many wireless communications systems, e.g. in systems under Nakagami-m fading. In this Letter we obtain exact expressions for the probability density function (PDF) and the cumulative distribution function (CDF) of the sum of arbitrarily correlated gamma variables in terms of certain Lauricella functions. Index Terms Gamma ...

The Laguerre method for the numerical inversion of Laplace transforms is a well known approach to the approximation of probability density functions (PDFs) and cumulative distribution functions (CDFs) of first passage times in Markov chains. Results are presented that relate the Laguerre generating functions and Laguerre coefficients of a PDF with those of the corresponding complementary CDF. T...

One of the conventional methods for temporary support of tunnels is to use steel sets with shotcrete. The nature of a temporary support system demands a quick installation of its structures. As a result, the spacing between steel sets is not a fixed amount and it can be considered as a random variable. Hence, in the reliability analysis of these types of structures, the selection of an appropri...

This paper proposes a method for probabilistic load flow in networks with wind generation, where the uncertainty of the production is non-Gaussian. The method is based on the properties of the cumulants of the probability density functions (PDF) and the Cornish–Fisher expansion, which is more suitable for non-Gaussian PDF than other approaches, such as Gram–Charlier series. The paper includes e...

In this paper the Weibull fading channel model is described and some integral characteristics of Weibull distribution are analyzed. For analytical and numerical evaluation of system performance, the Weibull probability density functions (pdf) are analyzed like particular solutions of corresponding differential equation, while the existence of singular solution is considered and analyzed under d...

An argument of common probability density function (pdf) is generally a real number, which describes the density, or mass in case of discrete random variable, of a random variable. However, in some applications, the pdf can be a complex function, so called complex probability density function. This kind of pdf is then, as general complex function, characterized by the amplitude and phase and is...

-In this paper, the k-μ random variable will be considered and closed form expressions for probability density function (PDF), cumulative distribution function (CDF) and moments for this distribution will be derived. Also, product, ratio, maximum and minimum of two k-μ random variables will be studied and PDFs of these functions calculated in the closed forms. Then, obtained statistical functio...

Supervised relational learning over labeled graphs, e.g. via recursive neural nets, received considerable attention from the connectionist community. Surprisingly, with the exception of recursive self organizing maps, unsupervised paradigms have been far less investigated. In particular, no algorithms for density estimation over graphs are found in the literature. This paper introduces first a ...

Fusing probabilistic information is a fundamental task in signal and data processing with relevance to many fields of technology science. In this work, we investigate the fusion multiple probability density functions (pdfs) continuous random variable or vector. Although case variables problem pdf frequently arise multisensor processing, statistical inference, machine learning, universally accep...