Random Number Generator - Log Pearson Type III Distribution

• State: CO
• Date: 2/15/2007
• Author: Anthony's VBA Page
• Title: Random Number Generator - Log Pearson Type III Distribution
• Water Supply Pro - Doc Type: Data

Random Number Generator - Log Pearson Type III Distribution Page 1 of 3
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Random Number Generator - Log Pearson Type III Distribution kJ
The Log Pearson Type III distribution is commonly used in h4raulic studies. It is s similar
to normal distribution, except instead of two parameters, stana�d 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).
ut
C' 1
(^ 2
3
Alpha 1 Tell)
5.00
5.00%
5.00%
Iteration
10000
10000
10000
Mean
10
10
10
SD
2
2
2
dfl
8.08
7.38
6.70
Skew
2
1
0.001
df2
F Populate simulated deviate on spreadsheet (65535 limit)
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).
output
Skew
2.26
1.06
-0.01
Mean
9.99
10.01
10.01
Sd
2.03
2.01
2.01
min
7.80
6.09
2.41
Max
34.76
24.68
17.75
Lower CI
8.08
7.38
6.70
UppercI
13.96
13.76
13.27
The following shows the charts generated from the 3 simulations. The charts
show as skew decreases, the distribution becomes more normal.
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http:// www. anthony- vba.kefra.com/vba /vbar6.htm 2/15/2007