Extended Generalized Functions and Its Distributions Applications. Book discusses the centrality of Extended Generalized gamma, beta functions, and distributions in its and applications

      Аннотация: The continuous distribution’s samples and their historical sequences in addition to the positive results they achieved within several practical applications in various productive and planning aspects are very important. It is notable that there is negligence in shaping the form of those continuous distributions. The multiple varieties of studied aspects make those samples and some of their mixtures which proved themselves during the last decade in many productive studies. The common assumption during the last period of time which says that the samples we study might be considered pure under some conditions which are not enough and impossible to achieve in addition of being very expensive and lately became very far from reality and that was affirmed by most of the studied samples. The researcher suggested the form which produces forms and various continuous distributions mixtures within several information values, which is the idea of the researcher in order to find the most general formula for various forms used in for the continuous distribution . The general gamma distribution model is considered as one of such distributions which established their role since it is shown

Ключевые слова: Mixture, Euler gamma function, recurrence formula, integral expression, density function, Special Functions, Stirling formula, extended gamma functions, completely monotonic functions, diffraction theory. Euler gamma function, extended expression gamma functions, extended generalized gamma distribution, special distributions, mixture distributions