Example 5.20 Displaying a Lognormal Reference Line

[See CAPPROB3 in the SAS/QC Sample Library]This example is a continuation of Creating Lognormal Probability Plots. Figure 5.18.8 shows that a lognormal distribution with shape parameter is a good fit for the distribution of Diameter in the data set Rods.

The lognormal distribution involves two other parameters: a threshold parameter and a scale parameter . See Table 5.62 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=plus height=3.5pct;
title 'Lognormal Probability Plot for Diameters';
proc capability data=Rods noprint;
   probplot Diameter / lognormal(sigma=0.5 theta=est zeta=est)
                       square
                       pctlminor
                       href      = 95
                       hreflabel = '95%'
                       vref      = 5.8 to 6.0 by 0.1
                       chref     = red
                       cvref     = blue;
run;

The plot is shown in Output 5.20.1.

Output 5.20.1 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 th percentile of the lognormal distribution. The HREFLABEL= option specifies 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 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.