Random
Number Generator - Log Pearson Type III Distribution

The
Log Pearson Type III distribution is commonly used in hydraulic
studies. It is somehow similar to normal distribution, except instead
of two parameters, stanand deviation and mean, it also has skew.
When the skew is small, Log Pearson Type III distribution approximates
normal.

The following example shows input and output from 3 simulations. Each has the same mean and standard deviation, but with different skew. The objective is to show the change in the distribution when skew changes. All three simulations have 10,000 iterations and alpha of 5% (for 1 tail test).

The following example shows input and output from 3 simulations. Each has the same mean and standard deviation, but with different skew. The objective is to show the change in the distribution when skew changes. All three simulations have 10,000 iterations and alpha of 5% (for 1 tail test).

The
output shows the estimate of skewness, mean, stand deviation, maximum
value, minimum value, lower confidence interval, and upper confidence
interval from each of the 3 simulations (these returned estimates can
be used to check it the random numbers generator works the way it is
instructed to do).

The following shows the charts generated from the 3 simulations. The charts show as skew decreases, the distribution becomes more normal.

* Complete program (with open source codes) available in Package Set 2 and the Combo Package.