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Discrete approximation of continuous distributions obtained by minimizing the weighted Cramer-von Mises distance
No full textDiscretization of Continuous Random Distributions Based on the Minimization of a Statistical Distance between Cumulative Distribution Functions
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Approximate evaluation of the distribution of the random sum of I.I.D. random variables through a discretization approach
Full text linkPortfolio allocation using multivariate variance gamma models
No full textIn this paper we investigate empirically the effect of using higher moments in portfolio allocation when parametric and non parametric models are used. The non parametric model considered in this paper is the sample approach while the parametric one is constructed assuming Multivariate Variance Gamma (MVG henceforth) joint distribution for asset returns. We consider the MVG models proposed by Madan and Seneta (1990), Semeraro (2006) and Wang (2009).We perform an out-of-sample analysis comparing the optimal portfolios obtained using the MVG models and the sample approach. Our portfolio is composed of 18 assets selected from the S&P500 Index and the dataset consists in daily returns observed in the period ranging from 01/04/2000 to 01/09/201
Goodman and Kruskal’s gamma coefficient for ordinalized bivariate distributions
Full text linkWe consider a bivariate normal distribution with linear correlation ρ whose random components are discretized according to two assigned sets of thresholds. On the resulting bivariate ordinal random variable, one can compute Goodman and Kruskal’s gamma coefficient, γ, which is a common measure of ordinal association. Given the known analytical monotonic relationship between Pearson’s ρ and Kendall’s rank correlation τ for the bivariate normal distribution, and since in the continuous case, Kendall’s τ coincides with Goodman and Kruskal’s γ, the change of this association measure before and after discretization is worth studying. We consider several experimental settings obtained by varying the two sets of thresholds, or, equivalently, the marginal distributions of the final ordinal variables. This study, confirming previous findings, shows how the gamma coefficient is always larger in absolute value than Kendall’s rank correlation; this discrepancy lessens when the number of categories increases or, given the same number of categories, when using equally probable categories. Based on these results, a proposal is suggested to build a bivariate ordinal variable with assigned margins and Goodman and Kruskal’s γ by ordinalizing a bivariate normal distribution. Illustrative examples employing artificial and real data are provided
Comparing approaches for approximating continuous random distributions with application in reliability engineering
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