(1.1) { Γ(α)Ψ(α,α−γ+1;ξ) }−1 exp(−ξv)v(1+v), v > 0, (1.2) respectively, where α > 0, β > 0, ξ > 0, −∞ < γ,λ < ∞, 1F1, and Ψ are confluent hypergeometric functions. These distributions are extensions of Gamma and Beta distributions, and for α < 1 (and certain values of λ and γ) yield bimodal distributions on finite and infinite ranges, respectively. These distributions are used (i) in the Bayesi...

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 ...

This paper compares the active and passive projector nonlinear gamma compensation methods for phase error reduction. The active method modifies fringe patterns before their projection to ensure sinusoidality; the passive method, in contrast, compensates for the phase error after capturing those distorted sinusoidal fringe patterns. Our study finds that the active method tends to provide more co...

In this paper we establish lower bounds on information divergence from a distribution to certain important classes of distributions as Gaussian, exponential, Gamma, Poisson, geometric, and binomial. These lower bounds are tight and for several convergence theorems where a rate of convergence can be computed, this rate is determined by the lower bounds proved in this paper. General techniques fo...

Two representations of the extended gamma functions Γ 2,0 0,2 [(b, x)] are proved. These representations are exploited to find a transformation relation between two Fox's H-functions. These results are used to solve Fox's H-function in terms of Meijer's G-function for certain values of the parameters. A closed form representation of the kernel of the Bessel type integral transform is also proved.

In this note we present a method for obtaining a wide class of combinatorial identities. We give several examples, in particular, based on the Gamma and Beta functions. Some of them have already been considered by previously, and other are new.

We calculated numerically the values of L-functions of four typical elliptic curves in the critical strip in the range Im(s) ≤ 400. We found that all the non-trivial zeros in this range lie on the critical line Re(s) = 1 and are simple except the one at s = 1. The method we employed in this paper is the approximate functional equation with incomplete gamma functions in the coefficients. For inc...

In this paper, we propose a novel method for detecting and segmenting text layers in complex images. This method is robust against degradations such as shadows, non-uniform illumination, low-contrast, large signaldependent noise, smear and strain. The proposed method first uses a geodesic transform based on a morphological reconstruction technique to remove dark/light structures connected to th...

The exponentiated gamma (EG) distribution is one of the important families of distributions in lifetime tests. In this paper, a new generalized version of this distribution which is called Transmuted exponentiated gamma (TEG) distribution is introduced. A new distribution is more flexible and has some interesting properties. A comprehensive mathematical treatment of the TEG distribution is prov...