In this work, we introduce a novel generalization of the extended exponential distribution with four parameters through Kumaraswamy family. The proposed model is referred to as (KwEE). significance suggested from its flexibility in applications and data modeling. As specific sub-models, it includes exponential, Lindley, exponentiated gamma generalized distributions. representation density funct...

In this paper, we consider admissible estimation of the parameter ?r in the gamma distribution with truncated parameter space under entropy loss function. We obtain the classes of admissible estimators. The result can be applied to estimation of parameters in the normal, lognormal, pareto, generalized gamma, generalized Laplace and other distributions.

The Oseen operators are ∆∂xj ∂xke , where ∆ is the standard Laplace operator and t ∈ R+. We give an explicit expression for the kernels of these Fourier multipliers which involves the incomplete gamma function and the confluent hypergeometric functions of the first kind. This explicit expression provides directly the classical decay estimates with sharp bounds. Although the computations are ele...

We present a new closed-form formula for the ergodic capacity of multiple-input multiple-output (MIMO) wireless channels. Assuming independent and identically distributed (i.i.d.) Rayleigh flat-fading between antenna pairs and equal power allocation to each of the transmit antennas, the channel capacity is expressed in closed form as finite sums of the exponential integrals which are the specia...

In this paper we count the number of paths and cycles in complete graphs by using the number e. Also, we compute the number of derangements in same way. Connection by e yields some nice formulas for the number of derangements, such as Dn = ⌊ n!+1 e ⌋ and Dn = ⌊(e + e −1)n!⌋ − ⌊en!⌋, and using these relations allow us to compute some incomplete gamma functions and hypergeometric summations; thes...

We present a formula that turns power series into series of functions. This formula serves two purposes: first, it helps to evaluate some power series in a closed form; second, it transforms certain power series into asymptotic series. For example, we find the asymptotic expansions for λ > 0 of the incomplete gamma function γ(λ,x) and of the Lerch transcendent Φ(x,s,λ). In one particular case, ...

X-linked severe combined immunodeficiency (XSCID) is a lethal disease caused by a defect in the gene encoding the common gamma chain (gamma-c) of the receptor for interleukin-2 (IL-2), IL-4, IL-7, IL-9, and IL-15. Allogeneic bone marrow transplantation, the current therapy of choice for this defect, is often complicated by graft-versus-host disease and/or incomplete reconstitution of B-lymphocy...