arXiv subjects

Franco Pellerey

Publications and source records attributed to Franco Pellerey.

3 recordsLinked to original sources

arXiv2024

On sums of dependent random lifetimes under the Time Transformed Exponential model

Considered a pair of random lifetimes whose dependence is described by a Time Transformed Exponential model, we provide analytical expressions for the distribution of their sum. These expressions are obtained by using a representation of the joint distribution in terms of multivariate distortions, which is an alternative approach to the classical copula representation. Since this approach allows to obtain conditional distributions and their inverses in simple form, then it is also shown how it can be used to predict the value of the sum from the value of one of the variables (or vice versa) by using quantile regression techniques.

math.ST↗

arXiv2023

Generalized Gini's mean difference through distortions and copulas, and related minimizing problems

Given a random variable $X$ and considered a family of its possible distortions, we define two new measures of distance between $X$ and each its distortion. For these distance measures, which are extensions of the Gini's mean difference, conditions are determined for the existence of a minimum, or a maximum, within specific families of distortions, generalizing some results presented in the recent literature.

math.PR↗

arXiv2012

Comparison results for Garch processes

We consider the problem of stochastic comparison of general Garch-like processes, for different parameters and different distributions of the innovations. We identify several stochastic orders that are propagated from the innovations to the Garch process itself, and discuss their interpretations. We focus on the convex order and show that in the case of symmetric innovations it is also propagated to the cumulated sums of the Garch process. More generally, we discuss multivariate comparison results related to the multivariate convex and supermodular order. Finally we discuss ordering with respect to the parameters in the Garch (1,1) case. Key words: Garch, Convex Order, Peakedness, Kurtosis, Supermodularity.

q-fin.ST↗