Improved near-exact distributions for the product of independent Generalized Gamma random variables

The Generalized Gamma distribution is an important distribution in Statistics since it has as particular cases many well known and important distributions and also due to its very interesting modeling properties, which makes it an attractive tool. The distribution of the product of independent Generalized Gamma distributions is investigated. Most of the results available for this distribution are based on Meijer-G or H functions which may still be very difficult to handle. Therefore, near-exact distributions which are based on the Generalized Near-Integer Gamma distribution and which have density and cumulative distribution functions easily implementable and computationally appealing are developed. Numerical studies with computationally intensive analyses are carried out to study the accuracy of these approximations in different scenarios. Also computational modules are provided for the implementation of these approximations. Finally, an example of application to quality control in microbiology is provided.