More on M.M. Zenga's new three-parameter distribution for nonnegative variables

Recently Zenga (2010) has proposed a new three-parameter density function f ðx : ; ; Þ, ( > 0; > 0; > 0), for non-negative variables. The parameter is equal to the expectation of the distribution. The new density has positive asymmetry and Paretian right tail. For > 1, Zenga (2010) has obtained the expressions of: the distribution function, the moments, the truncated moments, the mean deviation and Zenga’s (2007a) point inequality AðxÞ at x ¼ . In the present paper, as to the general case > 0, the expressions of: the distribution function, the ordinary and truncated moments, the mean deviations and Zenga’s point inequality AðÞ are obtained. These expressions are more complex than those previously obtained for > 1 by Zenga (2010). The paper is enriched with many graphs of: the density functions (0:5 1:5), the Lorenz LðpÞ and Zenga’s I ðpÞ curves as well as the hazard and survival functions.