More on M.M. Zenga’s new three-parameter distribution for nonnegative variables
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SUMMARY
Recently Zenga (2010) has proposed a new three-parameter density function f (x : µ; α; θ), (µ > 0; α > 0; θ > 0), for non-negative variables. The parameter µ is equal to the expectation of the distribution. The new density has positive asymmetry and Paretian right tail. For θ > 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 A(x) at x = µ. In the present paper, as to the general case θ > 0, the expressions of: the distribution function, the ordinary and truncated moments, the mean deviations and Zenga’s point inequality A (µ) are obtained. These expressions are more complex than those previously obtained for θ > 1 by Zenga (2010). The paper is enriched with many graphs of: the density functions (0.5 ≤ θ ≤ 1.5), the Lorenz L(p) and Zenga’s I (p) curves as well as the hazard and survival functions. Keywords: Non-Negative Variables, Positive Asymmetry, Paretian Right Tail, Beta Function, Lorenz Curve, Zenga’s Inequality Curve, Hazard Function, Survival Function. |
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