In this book we define univariate and bivariate gamma-type
distributions and discuss some of their statistical functions,
including the moment generating function. Numerous distributions
such as the Rayleigh, half-normal and Maxwell distributions can be
obtained as special cases. The moment generating function of both
univariate and bivariate random variables are derived by making use
of the inverse Mellin transform technique and expressed in terms of
generalized hypergeometric functions. These representations provide
computable expressions for the moment generating functions of
several of the distributions that were identified as particular
cases. Some other statistical functions are also given in closed
form. The univariate distribution is utilized to model two data
sets. This model provides a better fit than the two-parameter
Weibull model or its shifted counterpart, as measured by the
Anderson-Darling and Cramer-von Mises statistics.
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