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.

Zenga, M., Pasquazzi, L., Polisicchio, M., Zenga, M. (2011). More on M.M. Zenga's new three-parameter distribution for nonnegative variables. STATISTICA & APPLICAZIONI, 9(1), 5-33.

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

ZENGA, MICHELE;PASQUAZZI, LEO;POLISICCHIO, MARCELLA;ZENGA, MARIANGELA
2011

Abstract

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.
Articolo in rivista - Articolo scientifico
Non-Negative Variables, Positive Asymmetry, Paretian Right Tail, Beta Function, Lorenz Curve, Zenga’s Inequality Curve, Hazard Function, Survival Function
English
2011
9
1
5
33
none
Zenga, M., Pasquazzi, L., Polisicchio, M., Zenga, M. (2011). More on M.M. Zenga's new three-parameter distribution for nonnegative variables. STATISTICA & APPLICAZIONI, 9(1), 5-33.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/27479
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