Note: See Creating Lognormal Probability Plots in the SAS/QC Sample Library.
This example is a continuation of Creating Lognormal Probability Plots. Figure 5.36 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 .
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 odstitle = title; run;
The plot is shown in Output 5.20.1.
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 95th 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 CHREF= and CVREF= options specify colors for the horizontal and vertical reference lines.
Based on the intersection of the diagonal reference line with the HREF= line, the estimated 95th 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.