The issue of the mean signal level crossing rate for various probability density functions with primary relevance for optics is discussed based on a new analytical method. This method relies on a unique transformation that transforms the probability distribution under investigation into a normal probability distribution, for which the distribution of mean level crossings is known. In general, t...

REPORTRAPPORT Uniform asymptotics for the incomplete gamma functions starting from negative values of the parameters Abstract We consider the asymptotic behavior of the incomplete gamma functions (?a; ?z) and ?(?a; ?z) as a ! 1. Uniform expansions are needed to describe the transition area z a, in which case error functions are used as main approximants. We use integral representations of the i...

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 ...

Five of the six univariate natural exponential families (NEF) with quadratic variance functions (QVF), meaning their variances are at most quadratic functions of their means, are the Normal, Poisson, Gamma, Binomial, and Negative Binomial distributions. The sixth is the NEFCHS, the NEF generated from convolved Hyperbolic Secant distributions. These six NEF-QVFs and their relatives are unified i...

The secrecy performance is analyzed for a two-hop mixed radio frequency (RF)/underwater wireless optical communication (UWOC) system using decode-and-forward (DF) relay. All RF and UWOC links are modeled by the $\alpha -\mu $ exponent...

although there exist advanced models which predict beach profile for natural beaches, the behavior of the beaches in front of seawalls still suffers from the lack of appropriate theoretical models and sufficient measured data. in this paper, following the results obtained from the measurements, a beach profile evolution model is developed, using the measured probability distribution of the near...

This paper aims to evaluate the accuracy of probability calculation using Chebyshev’s inequality based on simulation study. We consider symmetric (Normal (3,1.52 ), Laplace (3, 2 ) Beta (7.7 t5) positively skewed, negatively skewed (5 χ2, 8 Gamma (5,1)), (Beta (7, 2)), Exponential (5) and Uniform (0, 1 distributions, fx(x) in our study measure performance inequality. then calculate Pr (μ − kσ ≤...

The α-μ distribution is a generalized fading distribution which explores nonlinearities of the wireless propagation medium. This distribution includes the other distributions such as Gamma, Nakagami, exponential, Gaussian, Rayleigh etc. This makes α-μ distribution very interesting. In this paper probability density function and performance metrics such as outage and bit error rate of α-μ distri...