On the Characteristic Function of the Four-Parameter Generalized Beta of the Second Kind (GB2) Distribution and Its Approximation to the Singh-Maddala, Dagum, and Fisk Distributions

Warsono
Kurniasari, Dian

Science and Technology Indonesia
Vol. 10 No. 1 (2025): January

Researchers have thoroughly investigated generalized distributions due to their inherent flexibility, which allows them to include several well-known distributions as special cases. Among these, the four parameter Generalized Beta of the Second Kind (GB2) distribution stands out as one of the most versatile frameworks in probability theory. Despite its broad applications, the GB2 distribution’s characteristic function, a critical tool in probability and statistical analysis, lacks a closed-form solution in the existing literature. This study pursues two primary objectives: first, to derive the characteristic function and the kth moment of the GB2 distribution, and second, to demonstrate how the GB2 distribution can serve as a close approximation to the Singh-Maddala, Dagum, and Fisk distributions using its characteristic function and kth moment. These derivations and approximations rely on gamma and beta functions, supplemented by the Maclaurin series expansion.