Mañana, JUEVES, 24 DE ABRIL, el sistema se apagará debido a tareas habituales de mantenimiento a partir de las 9 de la mañana. Lamentamos las molestias.
Percentiles of sums of heavy-tailed random variables: Beyond the single-loss approximation
Entity
UAM. Departamento de Ingeniería Informática; UAM. Departamento de MatemáticasPublisher
Springer USDate
2014-05Citation
10.1007/s11222-013-9376-6
Statistics and Computing 24.3 (2014): 377 – 397
ISSN
0960-3174 (print); 1573-1375 (online)DOI
10.1007/s11222-013-9376-6Funded by
The authors thank the anonymous reviewers for their valuable comments and suggestions. A.S. acknowledges financial support from the Spanish Dirección General de Investigación, project TIN2010-21575-C02-02.Editor's Version
http://dx.doi.org/10.1007/s11222-013-9376-6Subjects
Subexponential distributions; Heavy tails; Percentile estimation; Aggregate loss distribution; Censored moments; Value at Risk; Informática; MatemáticasNote
The final publication is available at Springer via http://dx.doi.org/10.1007/s11222-013-9376-6Rights
© Springer-Verlag Berlin Heidelberg 2014Abstract
A perturbative approach is used to derive
approximations of arbitrary order to estimate high percentiles
of sums of positive independent random variables
that exhibit heavy tails. Closed-form expressions
for the successive approximations are obtained both
when the number of terms in the sum is deterministic
and when it is random. The zeroth order approximation
is the percentile of the maximum term in the
sum. Higher orders in the perturbative series involve
the right-truncated moments of the individual random
variables that appear in the sum. These censored moments
are always finite. As a result, and in contrast
to previous approximations proposed in the literature,
the perturbative series has the same form regardless of
whether these random variables have a finite mean or
not. For high percentiles, and specially for heavier tails,
the quality of the estimate improves as more terms are
included in the series, up to a certain order. Beyond
that order the convergence of the series deteriorates.
Nevertheless, the approximations obtained by truncating
the perturbative series at intermediate orders are
remarkably accurate for a variety of distributions in a
wide range of parameters.
Files in this item
Google Scholar:Hernández, Lorenzo
-
Tejero, Jorge
-
Suárez González, Alberto
-
Carrillo Menéndez, Santiago
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