General

You can estimate Weibull parameters (shift, shape, scale) from estimates of the lower limit, most likely, upper limit and probability of excess over upper limit. You can estimate GPD (Generalised Pareto Distribution) parameters from two points on the cumulative distribution curve which we describe as the "VAR" point and the "Catastrophe" point.

For the Weibull you can also input a set of data points by pasting them into the text box (making sure there are no blank lines, especially at the end) to obtain a "first guess" estimate of the parameters. In due course there will be an exact curve fitting facility.

By pressing the calculate button the curve parameters are calculated and entered into the text boxes on the right.

You may also directly input into those text boxes using external information.

Probabilities and Inverse probabilities

However the (shift), shape and scale parameters are input, they may be used to calculate the probability of a value in excess of a specified value. A good test of the system is to check that if a VAR and probability have been entered to calculate the parameters, using the same parameters the calculated value of the probability of VAR is the original value on the left.

For the Weibull distribution, you input the items shown in red on the above diagram, and the shape and scale are computed for you. The shift parameter is input already as the "Lower Limit".

For the GPD distribution, you need to input two points on the curve: a "VAR" value and its associated probability and a "Catastrophe" value and its associated probability. The shape and scale parameters are then calculated.

Monte Carlo

Monte Carlo generates random samples (of up to 1000 items) for the following three distributions:

- Weibull distribution;
- GPD distribution;
- Actuarial which is an actuarial compound distribution based on an average rate as specified (using a Poisson distribution) and the Weibull severity distribution. The result is the overall compound distribution - a random sum of random values.

If you want to generate more items and put these into an organisational structure you need to purchase our Op Risk support software package - OpSim+. Contact us for details.

For more information or queries use the contact form or post a question on the bulletin board