Weighted generalized beta distribution of the second kind and related distributions

In this paper, a new class of weighted generalized beta distribution of the second kind (WGB2) is presented. The construction makes use of the conservability approach which includes the size or length-biased distribution as a special case. The class of WGB2 is used as descriptive models for the distribution of income. The results that are presented generalizes the generalized beta distribution of second kind (GB2). The properties of these distributions including behavior of hazard functions, moments, variance, coefficients of variation, skewness and kurtosis are obtained. The moments of other weighted distributions that are related to WGB2 are obtained. Other important properties including entropy (generalized and beta) which are measures of the uncertainty in this class of distributions are derived and studied.