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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.