CLOSED FORM EXPRESSIONS OBTAINED FROM THE SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS OF THE PROBABILITY DENSITY FUNCTION OF THE BETA DISTRIBUTION

Olasunmbo O.Agboola; Hilary I.Okagbue; Adedayo F.Adedotun; Paulinus O.Ugwoke

doi:10.17654/0974324322033

Olasunmbo O.Agboola Department of Mathematics, Covenant University, Ota, Nigeria
Hilary I.Okagbue Department of Mathematics, Covenant University, Ota, Nigeria
Adedayo F.Adedotun Department of Mathematics, Covenant University, Ota, Nigeria
Paulinus O.Ugwoke Department of Computer Science, University of Nigeria, Nsukka, Nigeria; Digital Bridge Institute, International Centre for Information, and Communications Technology Studies, Abuja, Nigeria

Article ID: 2562

DOI: https://doi.org/10.17654/0974324322033

Keywords: Beta distribution; closed form expression; ordinary differential equation; probability density function; shape parameter statistics

Abstract

In this paper, some closed form expressions for selected parameters for the probability density function (PDF) of the beta distribution are obtained. The closed form expressions are recovered from the solution of the ordinary differential equations (ODEs), obtained from the differentiation of the PDF of the distribution. The paper shows that the shape of the distributions also determines the nature of the resulting ODE which has shown how distributions related to the beta distribution can be traced via the solutions of the ODEs. Numerical methods are unnecessary because the closed form expressions are the same with the values obtained from the standard statistical software.

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