We consider the problem of a sum of two dependent and heavy tailed distributions through the C-convolution. The C-convolution provides the distribution of the sum of two random variables whose dependence structure is described by a copula function. Moreover, to investigate the role of heavy tails we use three different marginal distributions characterized by this property: Cauchy, Levy and Pareto. We show that the tail behavior of the C-convolution measured by level-q quantiles for q = 0.01, 0.05 (left tail) and q = 0.95, 0.99 (right tail) is strongly affected by the copula function which links the marginals and by the tail heaviness of marginals themselves.

Gobbi, F. (2018). Tail behavior of a sum of two dependence and heavy-tailed distributions. JOURNAL OF STATISTICS & MANAGEMENT SYSTEMS, 21(6), 933-953 [10.1080/09720510.2018.1461783].

Tail behavior of a sum of two dependence and heavy-tailed distributions

Gobbi F.
2018-01-01

Abstract

We consider the problem of a sum of two dependent and heavy tailed distributions through the C-convolution. The C-convolution provides the distribution of the sum of two random variables whose dependence structure is described by a copula function. Moreover, to investigate the role of heavy tails we use three different marginal distributions characterized by this property: Cauchy, Levy and Pareto. We show that the tail behavior of the C-convolution measured by level-q quantiles for q = 0.01, 0.05 (left tail) and q = 0.95, 0.99 (right tail) is strongly affected by the copula function which links the marginals and by the tail heaviness of marginals themselves.
Gobbi, F. (2018). Tail behavior of a sum of two dependence and heavy-tailed distributions. JOURNAL OF STATISTICS & MANAGEMENT SYSTEMS, 21(6), 933-953 [10.1080/09720510.2018.1461783].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11365/1118172