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 PROBPLOT Statement

## Example 9.2: Displaying a Lognormal Reference Line

 See CAPPROB3 in the SAS/QC Sample Library

This example is a continuation of "Creating Lognormal Probability Plots". Figure 9.4 shows that a lognormal distribution with shape parameter is a good fit for the distribution of DIAMETER in the data set MEASURES.

The lognormal distribution involves two other parameters: a threshold parameter and a scale parameter .See Table 9.13 for the equation of the lognormal density function. The following statements illustrate how you can request a diagonal distribution reference line whose slope and intercept are determined by estimates of and .

   symbol v=dot height=3.5pct;
legend2 frame cframe=ligr cborder=black position=center;
title 'Lognormal Probability Plot for Diameters';

proc capability data=measures noprint;
probplot diameter / lognormal(sigma=0.5 theta=est
zeta=est color=yellow w=2)
square
pctlminor
HREF=95
lHREF=2
hreflabel = '95%'
vref      = 5.8 to 6.0 by 0.1
lvref     = 3
cframe    = ligr
legend    = legend2
cHREF=red
cvref     = blue;
run;


The plot is shown in Output 9.2.1.

Output 9.2.1: Lognormal Reference Line

The close agreement between the diagonal reference line and the point pattern indicates that the specific lognormal distribution with ,, and is a good fit for the diameter measurements. Specifying HREF=95 adds a reference line indicating the 95 th percentile of the lognormal distribution. The LHREF=and HREFLABEL= options specify the line type and a label for this line. The PCTLMINOR option displays minor tick marks on the percentile axis. The VREF= option adds reference lines indicating diameter values of 5.8, 5.9, and 6.0, and the LVREF= option specifies their line type.

Based on the intersection of the diagonal reference line with the HREF=line, the estimated 95 th percentile of the diameter distribution is 5.85 mm.

Note that you could also construct a similar plot in which all three parameters are estimated by substituting SIGMA=EST for SIGMA=0.5 in the preceding statements.

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