The beta (b5) distribution of Kind-5

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 nonlinear programming with an illustrative application provided.