Parameter Estimation and the Goodness-of-fit Test for the Multivariate Generalized Gamma Distribution

This paper proposes a new form of multivariate generalized gamma distribution and some properties. This study aims to develop the MGG distribution using cumulative data from the univariate distribution, estimate the parameters using the Berndt-Hall-Hall-Hausman algorithm, and develop a goodness-of-fit test for this distribution using Kolmogorov-Smirnov Test. Applications of parameter estimation and the goodness of fit test procedure are discussed using simulation and real data. The results of the simulation study illustrate that the proposed procedure can estimate the parameters of the MGG distribution reasonably. The distribution fit test can be done with the Chi-square test, with the number of variates as a degree of freedom. The empirical research results show that the three education indicators in Central Java, Indonesia, from 2017 to 2021, follow the MGG distribution.