Warsono, Warsono and Kurniasari, Dian (2025) 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. Science and Technology Indonesia, 10 (1). pp. 201-211. ISSN 25804391

Text On the Characteristic Function of the Four-Parameter Generalized Beta of the SecondKind (GB2) Distribution and Its Approximation to the Singh-Maddala, Dagum, and Fisk Distributions.pdf Download (1MB)

Abstract

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 k-th 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 k-th moment. These derivations and approximations rely on gamma and beta functions, supplemented by the Maclaurin series expansion.

Item Type:	Article
Subjects:	Q Science > QA Mathematics
Divisions:	Fakultas Matematika dan Ilmu Pengetahuan Alam (FMIPA) > Prodi Matematika
Depositing User:	DIAN KURNIASARI
Date Deposited:	24 Feb 2025 07:31
Last Modified:	24 Feb 2025 07:31
URI:	http://repository.lppm.unila.ac.id/id/eprint/54431

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