A New Family of Distributions: Libby-Novick Beta

Abstract

We define a family of distributions, named the Libby-Novick beta family of distributions, which includes the classical beta generalized and exponentiated generators. The new family offers much more flexibility for modeling real data than these two generators and the Kumaraswamy family of distributions (Cordeiro & de Castro, 2011). The extended family provides reasonable parametric fits to real data in several areas because the additional shape parameters can control the skewness and kurtosis simultaneously, vary tail weights and provide more entropy for the generated distribution. For any given distribution, we can construct a wider distribution with three additional shape parameters which has much more flexibility than the original one. The family density function is a linear combination of exponentiated densities defined from the same baseline distribution. The proposed family also has tractable mathematical properties including moments, generating function, mean deviations and order statistics. The parameters are estimated by maximum likelihood and the observed information matrix is determined. The importance of the family is very well illustrated. By means of two real data sets we demonstrate that this family can give better fits than those ones using the McDonald, beta generalized and Kumaraswamy generalized classes of distributions.