In this paper, we propose two new generalized gamma-generated distributions with any base distribution. In particular, we obtain the generalized gamma-
generated exponential Weibull distribution (GG-EW) and generalized gamma-generated Dagum distribution (GG-Dagum). We study some mathematical properties of the new distributions, including explicit formulas for the probability density function, cumulative distribution function, by using Gauss' hypergeometric and Meijer G functions. It is shown, in general, that the generalized gamma-generated distributions are innite linear combinations of the powers of the base distribution. Incorrect results given earlier by other authors are pointed out. We applied the distributions in the following data sets: (a) spending on public education in various countries in 2003 and (b) total expenditure on health in 2009 in various countries. The results show that the distributions t well the data sets. The general R codes for tting the distributions introduced in this paper are given in Appendix.
Keywords and Phrases
Exponentiated Weibull distribution, Dagum distribution, gamma-generated distribution, special functions.
A.M.S. subject classiﬁcation
60E05, 62B15, 33C60, 60E10