In this paper, we prove that for $s\in(0,\infty)$, the harmonic mean of $E_k(s)$ and $E_k(1/s)$ is always less than or equal to $\Gamma(1-k,1)$. Where generalized exponential integral function, $\Gamma(u,s)$ upper incomplete gamma function $k\in \mathbb{N}$.

A Fortran 90 module GammaCHI for computing and inverting the gamma and chi-square cumulative distribution functions (central and noncentral) is presented. The main novelty of this package are the reliable and accurate inversion routines for the noncentral cumulative distribution functions. Additionally, the package also provides routines for computing the gamma function, the error function and ...

in this paper, a bayesian approach is proposed for shift point detection in an inverse gaussian distribution. in this study, the mean parameter of inverse gaussian distribution is assumed to be constant and shift points in shape parameter is considered. first the posterior distribution of shape parameter is obtained. then the bayes estimators are derived under a class of priors and using variou...

objective(s) in this study we investigated the expression of gabaa receptor subunits during brain development. these receptors may change in the embryonic chick forebrain. materials and methodes the expression levels of four types of gabaa receptor gamma subunits (γ1, γ2, γ3 and γ4) were quantified in the embryonic chick forebrain at 32 hr, 3, 7, 14, and 20 days of incubation and day one after ...