26,355 research outputs found
A Short Tale of Long Tail Integration
Integration of the form , where is either
or , is widely
encountered in many engineering and scientific applications, such as those
involving Fourier or Laplace transforms. Often such integrals are approximated
by a numerical integration over a finite domain , leaving a truncation
error equal to the tail integration in addition
to the discretization error. This paper describes a very simple, perhaps the
simplest, end-point correction to approximate the tail integration, which
significantly reduces the truncation error and thus increases the overall
accuracy of the numerical integration, with virtually no extra computational
effort. Higher order correction terms and error estimates for the end-point
correction formula are also derived. The effectiveness of this one-point
correction formula is demonstrated through several examples
The Evolution of Cross-Region Price Distribution in Russia
The behavior of the entire cross-section distribution of prices in Russian regions is analyzed from 1992 through 2000, using non-parametric techniques. The cost of a staples basket is used as a price representative. Price dispersion measured as the standard deviation of prices is found to be diminishing since about 1994; and the shape of the cross-region distribution of prices tends to be more regular over time. To characterize intra-distribution mobility, a transition probability function (stochastic kernel) is estimated. It is also used to derive a long-run limit of the price distribution. Overall, the results suggest that, excluding a few years following the price liberalization, price convergence has been happening among Russian regions.http://deepblue.lib.umich.edu/bitstream/2027.42/40102/3/wp716.pd
Computing Tails of Compound Distributions Using Direct Numerical Integration
An efficient adaptive direct numerical integration (DNI) algorithm is
developed for computing high quantiles and conditional Value at Risk (CVaR) of
compound distributions using characteristic functions. A key innovation of the
numerical scheme is an effective tail integration approximation that reduces
the truncation errors significantly with little extra effort. High precision
results of the 0.999 quantile and CVaR were obtained for compound losses with
heavy tails and a very wide range of loss frequencies using the DNI, Fast
Fourier Transform (FFT) and Monte Carlo (MC) methods. These results,
particularly relevant to operational risk modelling, can serve as benchmarks
for comparing different numerical methods. We found that the adaptive DNI can
achieve high accuracy with relatively coarse grids. It is much faster than MC
and competitive with FFT in computing high quantiles and CVaR of compound
distributions in the case of moderate to high frequencies and heavy tails
Bacteriophages and their structural organisation
Viruses are extremely small infectious particles that are not visible in a light microscope, and
are able to pass through fine porcelain filters. They exist in a huge variety of forms and
infect practically all living systems: animals, plants, insects and bacteria. All viruses have a
genome, typically only one type of nucleic acid, but it could be one or several molecules of
DNA or RNA, which is surrounded by a protective stable coat (capsid) and sometimes by
additional layers which may be very complex and contain carbohydrates, lipids, and
additional proteins. The viruses that have only a protein coat are named ânakedâ, or non-
enveloped viruses. Many viruses have an envelope (enveloped viruses) that wraps around
the protein capsid. This envelope is formed from a lipid membrane of the host cell during
the release of a virus out of the cell
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
The Evolution of Cross-Region Price Distribution in Russia
The behavior of the entire cross-section distribution of prices in Russian regions is analyzed from 1992 through 2000, using non-parametric techniques. The cost of a staples basket is used as a price representative. Price dispersion measured as the standard deviation of prices is found to be diminishing since about 1994; and the shape of the cross-region distribution of prices tends to be more regular over time. To characterize intra-distribution mobility, a transition probability function (stochastic kernel) is estimated. It is also used to derive a long-run limit of the price distribution. Overall, the results suggest that, excluding a few years following the price liberalization, price convergence has been happening among Russian regions.price convergence, price dispersion, distribution dynamics, market integration, Russia
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