 # Loss Tools

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### Glossary

Aliasing
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.