First derivatives with respect to the parameters of Whittaker function $\mathrm{W}_{\kappa ,\mu }\left( x\right) $ are calculated. Using confluent hypergeometric function, these derivarives can be expressed as infinite sums quotients digamma and gamma functions. Also, it is possible obtain parameter in terms integrals integrands containing elementary functions (products algebraic, exponential l...

This article presents differential equations and solution methods for the functions of the form A(z) = F−1(G(z)), where F and G are cumulative distribution functions. Such functions allow the direct recycling of samples from one distribution into samples from another. The method may be developed analytically for certain special cases, and illuminate the idea that it is a more precise form of th...

In this paper, a modified exponentiated family of distributions is introduced. The new model was built from continuous parent cumulative distribution function and depends on shape parameter. Its most relevant characteristics have been obtained: the probability density function, quantile moments, stochastic ordering, Poisson mixture with our proposal as mixing distribution, order statistics, tai...

In this paper, we consider the issue of devising a flexible nonlinear function for multichannel blind deconvolution. In particular, we consider the underlying assumption of the source probability density functions. We consider two cases, when the source probability density functions are assumed to be uni-modal, and multimodal respectively. In the unimodal case, there are two approaches: Pearson...

This investigation deals with MX/G/1 queueing model with setup, bulk- arrival, loss-delay and balking. The provision of second optional service apart from essential service by an unreliable server is taken into consideration. We assume that the delay customers join the queue when server is busy whereas loss customers depart from the system. After receiving the essential service, the customers m...