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

J tJ 1.. J .,., '1

"

compute the mean, SO, and skew of the logs of the data ~y:= mean(y), cry:= Stdev(y), Cy:= skew(y)

Fitting data to an LP III distribution is somewhat analogous to fitting data to a log-normal distribution. If the
data itself fits an LP 3 distribution then the logs of the data will fit a Pearson III distribution. This is the same
procedure that is followed when trying to fit data to a log normal distribution, we fit the logs of the data to a
normal distribution.

The equations relating the distribution parameters, <x, p and E to the moments of the data are: A = ~ ,
cry

( 2 )2 P
p = - and E = ~y - -. These can be solved simultaneously for <x, p and E using a solve block.
Cy A

initial guesses for parameters E:= 1, p := 5, A:= 1

Given

A=~
cry

~ =( ~r

- P
E-~ --
Y A

soln := Find(A, p , E)

[4,844 ]
soln = 7.506
6.206

rename each element of the soln vector: A:= solnO, p := soln1 and E := soln2

Now plot the distribution using a range variable: y:= 1 , 1.1.. 10

~ ~-1
A '(y-E) ,exp[-A,(y-E)]
p(y) := r(P)

log pearson type III example problem
bulletin 17.mcd
last save 11/14/2003/12:01 PM

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

20t 5