WSPC63

• File Number: 8230.400.21
• Description: Colorado River Litigation - State, Division 4 Water Court Cases - Steamboat RICD
• State: CO
• Basin: Yampa/White
• Water Division: 6
• Date: 11/14/2003
• Author: Ray Alvarado
• Title: The Log Pearson Type III Distribution - Bulletin 17 Data
• Water Supply Pro - Doc Type: Data

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III
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0.8
0.72
0.64
0.56
0.48
p( y) 0.4

0.32
0.24
0.16
0.08

o 6

LP III Probability Distribution

~ r-....
/ '\
II \
/ 1\
/ \
I \
/ \.
/ "
I "
~ ...... --

6.4 6.8 7.2 7.6 8 8.4 8.8 9.2 9.6 10
Y
In (flow)

The area under any probibility distribution curve must equal 1.0. This can be used as a check on the
procedure

f50
~ ~-1
A. ,(y - e) ,exp[-A.'(Y - e)]
1(~) dy=1
E

Check : Area under curve equals 1.0

Cumulative LP III distribution

In order to get a cumulative LP Type III distribution we can integrate the probability distribution from the
lower bound to some value x. The value obtained for each x is the probability that future flow values
will be less than or equal to that value of x.

yy := 1,1.1.. 10

fyy
~ ~-1
(A.) '(y - E) ,exp[-A.'(Y - e)]
cum_LP _III (yy) := dy
1(~)
E

cumulative LP III Distribution

In order to see how well the data actually fit the analytical distribution we will sort the logs of the data,
compute the respective probabilities and plot the data itself on the same set of axis as the cumulative
distribution.

log pearson type 11\ example problem
bulletin 17.mcd
last save 11/1412003/12:01 PM

30f5

C:\MyFiles\Mathcad application areas
\Statistics\log Pearson Type III aka Gamma
distribution files\
11/14/2003/12:07 PM