Finding alternative to most well known classical family of distributions has become a topic of high importance in academic research due to their striking properties. An increasing interest can be observed for the art of adding parameter to some existing distributions as one parameter family of distributions is not sufficient to handle various real contexts. There is a vast amount of literature ...

We present an efficient implementation of hypergeometric functions in arbitraryprecision interval arithmetic. The functions 0F1, 1F1, 2F1 and 2F0 (or the Kummer U -function) are supported for unrestricted complex parameters and argument, and by extension, we cover exponential and trigonometric integrals, error functions, Fresnel integrals, incomplete gamma and beta functions, Bessel functions, ...

The confluent hypergeometric beta distribution due to Gordy has been known since the 1990s, but not much of is in terms its mathematical properties. In this paper, we provide a comprehensive treatment properties distribution. We derive shape probability density function and expressions for cumulative function, hazard rate reversed moment generating characteristic moments, conditional entropies,...