## Example 4.33 Estimating Parameters from Lognormal Quantile Plots

This example, which is a continuation of Example 4.31, demonstrates techniques for estimating the shape, location, and scale parameters, and the theoretical percentiles for a two-parameter lognormal distribution.

If the threshold parameter is known, you can construct a two-parameter lognormal Q-Q plot by subtracting the threshold from the data values and making a normal Q-Q plot of the log-transformed differences, as illustrated in the following statements:

data ModifiedMeasures;
set Measures;
LogDiameter = log(Diameter-5);
label LogDiameter = 'log(Diameter-5)';
run;

symbol v=plus;
title 'Two-Parameter Lognormal Q-Q Plot for Diameters';
proc univariate data=ModifiedMeasures noprint;
qqplot LogDiameter / normal(mu=est sigma=est)
square
vaxis=axis1;
inset n mean (5.3) std (5.3)
/ pos = nw header = 'Summary Statistics';
axis1 label=(a=90 r=0);
run;

**
Output 4.33.1
Two-Parameter Lognormal Q-Q Plot for Diameters**

Because the point pattern in

Output 4.33.1 is linear, you can estimate the lognormal parameters

and

as the normal plot estimates of

and

, which are

0.99 and 0.51. These values correspond to the previous estimates of

0.92 for

and 0.5 for

from

Example 4.31. A sample program for this example,

*uniex18.sas*, is available in the SAS Sample Library for Base SAS software.

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