Closed Form Expressions Obtained From the Solution of Ordinary Differential Equations of the Probability Density Function of the Beta Distribution

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.