Effect where tail of probability distribution wraps
around and appears at beginning of distribution. This is the same effect that
makes wagon wheels appear to go backwards in movies.
Contagion
Method of specifying the variance of a frequency distribution. A negative
binomial distribution with mean m and contagion c has variance m(1+cm).
Density
Probability Density. In MALT most densities are
represented by vectors, (Pr(X=0), Pr(X=u), Pr(X=2u), ...) for some unit u.
If the x values are not evenly spaced the density is input as a
collection of pairs (x, Pr(x)).
Discretizing or Bucketting a Distribution
Process of converting from a continuous distribution
to a discrete distribution by computing the probability in evenly spaced
buckets. See Wang Sections 3.3.1 and 3.3.2. In this paper we only use the
rounding method.
Distribution
Pr(X<x), or cumulative density.
FFT, IFFT
Fast Fourier Transform and Inverse Fast Fourier
Transform. See Wang Section 2.2
How to input multiple arguments in one text box
Enter numbers separated by a space, tab, comma or
carriage return. Numbers can be entered in scientific notation
using E or e for the exponent.
ISO Parameters
The default parameter file has space for the common ISO AL and GL curves.
However, since ISO parameters are proprietary, all the built-in distributions
in the sample are in fact the same "reasonable" distribution. See the Appendix for information
on building your own parameter file, to incorporate your own proprietary data.
Num, Num_L2
Num represents the number of buckets used to
discretize a distribution. Num_L2 is the log of Num to base 2. So if
Num = 32, Num_L2 = 5, Num = 1024, Num_L2 = 10 and so forth.
All FFTs in MALT are computed using vectors whose length is a
power of 2, so it is natural to enter their length interms of a log to
base 2.
Sample
A random or non-random sample from a distribution. For
example 100 percentile points. The AIR cat model produces a 1,000 or 10,000
point samples from the distribution of losses.
Shifted Lognormal
The shifted lognormal is a distribution of the form T + lognormal(mu,
sigma). It has three parameters: T, mu and sigma. It is possible to
match the mean, CV and skewness using the shifted lognormal. Fitting using method
of moments is easy, using closed form equations.
Unit
The width of a bucket used to dicretize a
distribution. In most examples, setting Unit = 0 forces the model to
compute and display a reasonable value. If a non-zero number is input then it
is used, regardless of whether it is reasonable. This can cause weird results.
Variance Multiplier
Method of specifying the variance of a frequency distribution. A
distribution with mean m and variance multiplier v has variance
vm.