Marques, Filipe J.Loots, Mattheus TheodorBekker, Andriette, 1958-2020-06-052019-11Marques, F.J., Loots, M.T. & Bekker, A. Series representations for densities functions of a family of distributions—Application to sums of independent random variables. Mathematical Methods in Applied Sciences 2019;42: 5718–5735. https://doi.org/10.1002/mma.5463.0170-4214 (print)1099-1476 (online)10.1002/mma.5463http://hdl.handle.net/2263/74883Series representations for several density functions are obtained as mixtures of generalized gamma distributions with discrete mass probability weights, by using the exponential expansion and the binomial theorem. Based on these results, approximations based on mixtures of generalized gamma distributions are proposed to approximate the distribution of the sum of independent random variables, which may not be identically distributed. The applicability of the proposed approximations are illustrated for the sum of independent Rayleigh random variables, the sum of independent gamma random variables, and the sum of independent Weibull random variables. Numerical studies are presented to assess the precision of these approximations.en© 2019 John Wiley & Sons, Ltd. This is the pre-peer reviewed version of the following article : Series representations for densities functions of a family of distributions—Application to sums of independent random variables. Mathematical Methods in Applied Sciences 2019;42: 5718–5735. https://doi.org/10.1002/mma.5463. The definite version is available at : http://wileyonlinelibrary.com/journal/mma.Binomial theoremExponential expansionGeneralized gamma distributionMixturesPostprint Article