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Mariangela Zenga

Libri dell'autore

The Dagum distribution in reliability analisys
Gratis
digital
formato: Articolo | STATISTICA & APPLICAZIONI - 2012 - 2
Anno: 2012
SUMMARY This work proposes the use of the Dagum model (Dagum, 1977) in the reliability theory. The main motivation is that the hazard rate of this model is very flexible; in fact, it is proved (Domma, 2002) that, according to the values of the parameters, the hazard rate of the Dagum distribution has a decreasing, or an Upside-down Bathtub, or Bathtub and then Upside-down Bathtub failure rate. This work studies some features of the Dagum distribution as the reversed hazard rate, the mean and variance of the random variables residual life and reversed residual life and their monotonicity properties. Two published data sets have been analyzed for illustrative purposes. Keywords: Burr III distribution, Reversed Hazard Function, Mean Residual Life, Mean Waiting Time, Variance of Residual Life and Reversed Residual Life.
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First applications of a new three-parameter distribution for non-negative variables
Gratis
digital
formato: Articolo | STATISTICA & APPLICAZIONI - 2012 - 2
Anno: 2012
SUMMARY Zenga (2010a) recently proposed a new three-parameter family of density functions for non-negative variables. Its properties resemble those of economic size distributions: it has positive asymmetry, Paretian right tail and it may be zeromodal, unimodal or even bimodal. In this paper we explore some methods for fitting the new density to empirical income distributions. We will see that D’Addario’s invariants method clearly outperforms Pearson’s moments method, which does not seem to work well with heavy tailed distributions. Further, we propose some new methods based on the minimization of a measure for the goodness of fit, imposing restrictions on the parameter space to preserve some features of the empirical distribution in the fitted model. We will see that these methods provide very satisfactory results with income distributions from Italy, Swiss, US and UK. Keywords: Income Distribution, Zenga’s Distribution, Goodness of Fit, Moments Method, Invariants Method.
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More on M.M. Zenga’s new three-parameter distribution for nonnegative variables
Gratis
digital
formato: Articolo | STATISTICA & APPLICAZIONI - 2011 - 1
Anno: 2011
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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Bipolar mean and mean deviation about the bipolar mean for discrete quantitative variables digital
formato: Articolo | STATISTICA & APPLICAZIONI - 2006 - 1
Anno: 2006
In this paper, the bipolar mean, that can be seen as a frequencies distribution, has been extended to the discrete variables.
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