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The confluent hypergeometric-mixture of Polisicchio distributions: a generalized Zenga distribution
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format: Article | STATISTICA & APPLICAZIONI - 2013 - 1
Year: 2013
We propose a generalization of the three-parameters Zenga distribution obtaining a four-parameters model. The generalization is performed using the confluent hypergeometric distribution as mixing distributions in place of the classical beta. We compare the flexibility of the resulting model with that of the Zenga distribution observing some improvements.
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Zenga distribution: parameters estimation with constraints on synthetic inequality indices digital
format: Article | STATISTICA & APPLICAZIONI - 2014 - 1
Year: 2015
In 2010, Zenga introduced a three-parameter model for distributions by size, with Paretian right-tail and expectation always finite...
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The distribution of the absolute value of the ratio of two correlated normal random variables digital
format: Article | STATISTICA & APPLICAZIONI - 2015 - 1
Year: 2015
The aim of this paper is to study the distribution of the absolute quotient of two Correlated Normal random variables (r.v.s). This study may have many applications, as often the researcher expects a ratio to be positive or considers the sign of the ratio unimportant...
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On the distribution of the sum of cograduated discrete random variables with applications to credit risk analysis digital
format: Article | STATISTICA & APPLICAZIONI - 2015 - 1
Year: 2015
This paper focuses on the notion of cograduation which was first introduced in 1939 by the Italian statistician Tommaso Salvemini. In few words, a certain number of random variables are cograduated if they are associated with the maximum positive dependence. Here, it is shown how to derive the probability distribution of the sum of cograduated discrete random variables...
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A Generalized multivariate skew-normal distribution with applications to spatial and regression predictions digital
format: Article | STATISTICA & APPLICAZIONI - 2015 - 1
Year: 2015
In this paper, a generalization to the multivariate skew-normal distribution of Arnold and Beaver (2002) is proposed. Also several distributional properties of the proposed distribution are explored. The proposed distribution has been used to define a stochastic process called the generalized-skew Gaussian process...
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The turn of the screw. Changes in income distribution in Italy (2002-2010) digital
format: Article | STATISTICA & APPLICAZIONI - 2014 - 2
Year: 2015
This article uses data from the 2002-2010 waves of Bank of Italy Survey on Households Income and Wealth. It reports data on the evolution of the distribution of income by main households’ income sources and by households’ income rank and on the evolution of concentration indexes by the same characters...
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Maximum likelihood estimator of the shape parameter of the weibull distribution using ranked set sampling digital
format: Article | STATISTICA & APPLICAZIONI - 2013 - 2
Year: 2014
In this paper, we will consider the (maximum likelihood estimators) MLEs of the shape parameter p of the Weibull distribution...
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Application of Zenga’s distribution to a panel survey on household incomes of European Member States
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digital
format: Article | STATISTICA & APPLICAZIONI - 2013 - 1
Year: 2013
In this paper Zenga’s distribution is applied to 114 household incomes distributions from a panel survey conducted by Eurostat. Previous works showed the good behaviour of the model to describe income distributions and analyzed the possibility to impose restrictions on the parametric space so that the fitted models comply with some characteristics of interest of the samples. This work is the first application of the model on a wide number of distributions, showing that it can be used to describe incomes distributions of several countries. Maximum likelihood method on grouped data and methods based on the minimization of three different goodness of fit indexes are used to estimate parameters. The restriction that imposes the equivalence between the sample mean and the expected value of the fitted model is also considered. It results that the restriction should be used and the changes in fitting are analyzed in order to suggest which estimation method use jointly to the restriction. A final section is devoted to the direct proof that Zenga’s distribution has Paretian right-tail.
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The Dagum distribution in reliability analisys
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digital
format: Article | STATISTICA & APPLICAZIONI - 2012 - 2
Year: 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
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digital
format: Article | STATISTICA & APPLICAZIONI - 2012 - 2
Year: 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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The distribution model with linear inequality curve I(p)
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digital
format: Article | STATISTICA & APPLICAZIONI - 2011 - 1
Year: 2011
SUMMARY The aim of an important branch of inequality analysis is the investigation into the features of the distribution models with specific kinds of inequality curves. This paper is an investigation into the distribution model with linear inequality I ðpÞ curve. The definition of the corresponding distribution function, and a procedure to obtain the probability density function are described. An analysis of the constraints that the parameters of the line must satisfy is also provided. The methodological results are supported by two applications with real air traffic control data. Keywords: Inequality, Lorenz L(p) Curve, Zenga I (p) Curve, Income Distributions.
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Estimation of the variance for logistic distribution under ranked set sampling and simple random sampling: a comparative study
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digital
format: Article | STATISTICA & APPLICAZIONI - 2012 - 2
Year: 2012
SUMMARY The logistic distribution is applicable in many area of research. In this study, several estimators of the variance when the location parameter is known and unknown are considered when data are gathered under simple random sampling (SRS) and ranked set sampling (RSS). For some estimators considered, the bias and mean square error (MSE) are not gotten in closed form. Using Monte Carlo simulations, comparison of these estimators is made based on biases, MSE and efficiency. When the estimators are compared, it is found that estimators based on maximum likelihood method are more efficient than other estimators considered, under both SRS and RSS. However, estimators based on RSS have more advantages over those based on SRS. Keywords: Logistic Distribution, Ranked set Sampling, Simple Random Sampling, Variance, Estimations.
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