10,530 research outputs found
Calculation of aggregate loss distributions
Estimation of the operational risk capital under the Loss Distribution
Approach requires evaluation of aggregate (compound) loss distributions which
is one of the classic problems in risk theory. Closed-form solutions are not
available for the distributions typically used in operational risk. However
with modern computer processing power, these distributions can be calculated
virtually exactly using numerical methods. This paper reviews numerical
algorithms that can be successfully used to calculate the aggregate loss
distributions. In particular Monte Carlo, Panjer recursion and Fourier
transformation methods are presented and compared. Also, several closed-form
approximations based on moment matching and asymptotic result for heavy-tailed
distributions are reviewed
A Continuous Analogue of Lattice Path Enumeration: Part II
Here are exhibited some additional results about the continuous binomial
coefficients as introduced by L. Cano and R. Diaz in [1].Comment: second versio
Distance distribution in configuration model networks
We present analytical results for the distribution of shortest path lengths
between random pairs of nodes in configuration model networks. The results,
which are based on recursion equations, are shown to be in good agreement with
numerical simulations for networks with degenerate, binomial and power-law
degree distributions. The mean, mode and variance of the distribution of
shortest path lengths are also evaluated. These results provide expressions for
central measures and dispersion measures of the distribution of shortest path
lengths in terms of moments of the degree distribution, illuminating the
connection between the two distributions.Comment: 28 pages, 7 figures. Accepted for publication in Phys. Rev.
Characterization of count data distributions involving additivity and binomial subsampling
In this paper we characterize all the -parameter families of count
distributions (satisfying mild conditions) that are closed under addition and
under binomial subsampling. Surprisingly, few families satisfy both properties
and the resulting models consist of the th-order univariate Hermite
distributions. Among these, we find the Poisson () and the ordinary
Hermite distributions ().Comment: Published at http://dx.doi.org/10.3150/07-BEJ6021 in the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
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