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Open Access Research Article

The beta (b5) distribution of Kind-5

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pp. 285–299Vol. 29Issue 3March 2026DOI: 10.47974/JSMS-1490XML
Received:
11 Sep 2024
Published Online:
30 Dec 2025
Article type:
Research Article
Language:
EN
Article no.:
JSMS-1490
Pages:
285–299

Abstract

This paper introduces a beta distribution (BD) of Kind-5 with its density function expressed in terms of Gauss hypergeometrric function. Key distributional properties including the cumulative distribution function and the mandatory constants such as central moments, non-central moments, skewness, kurtosis, log-geometric mean, Harmonic mean, Shannon’s differential entropy are thoroughly examined. Additionally, the moment, cumulant, characteristic functions are derived. Special cases are explored through transformations of beta kind-5 variable and parameter shifting. The paper also covers parameter estimation using the method of unconstrained maximum likelihood estimation, the construction of Fisher’s information matrix and a constrained maximum likelihood approach by using non-linear programming with an illustrative application provided.

Keywords

Subject Classifications

62H1062G07

References

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