specifies the shape parameter for P-P plots requested with the BETA and GAMMA options. For examples, see the entries for the BETA and GAMMA options.

creates a beta P-P plot. To create the plot, the nonmissing observations are ordered from smallest to largest:

The -coordinate of the th point is the empirical cdf value . The -coordinate is the theoretical beta cdf value

where is the normalized incomplete beta function, , and

lower threshold parameter
scale parameter
first shape parameter
second shape parameter

You can specify , , , and with the ALPHA=, BETA=, SIGMA=, and THETA= beta-options, as illustrated in the following example:

proc capability data=measures;
   ppplot width / beta(theta=1 sigma=2 alpha=3 beta=4);
run;

If you do not specify values for these parameters, then by default, , , and maximum likelihood estimates are calculated for and .

IMPORTANT: If the default unit interval (0,1) does not adequately describe the range of your data, then you should specify THETA= and SIGMA= so that your data fall in the interval .

If the data are beta distributed with parameters , , , and , then the points on the plot for ALPHA=, BETA=, SIGMA=, and THETA= tend to fall on or near the diagonal line , which is displayed by default. Agreement between the diagonal line and the point pattern is evidence that the specified beta distribution is a good fit. You can specify the SCALE= option as an alias for the SIGMA= option and the THRESHOLD= option as an alias for the THETA= option.

specifies the shape parameter for P-P plots requested with the BETA distribution option. See the preceding entry for the BETA distribution option for an example.

specifies the shape parameter for P-P plots requested with the WEIBULL option. See the entry for the WEIBULL option for examples.

creates an exponential P-P plot. To create the plot, the nonmissing observations are ordered from smallest to largest:

The -coordinate of the th point is the empirical cdf value . The -coordinate is the theoretical exponential cdf value

where

threshold parameter
scale parameter

You can specify and with the SIGMA= and THETA= exponential-options, as illustrated in the following example:

proc capability data=measures;
   ppplot width / exponential(theta=1 sigma=2);
run;

If you do not specify values for these parameters, then by default, and a maximum likelihood estimate is calculated for .

IMPORTANT: Your data must be greater than or equal to the lower threshold . If the default is not an adequate lower bound for your data, specify with the THETA= option.

If the data are exponentially distributed with parameters and , the points on the plot for SIGMA= and THETA= tend to fall on or near the diagonal line , which is displayed by default. Agreement between the diagonal line and the point pattern is evidence that the specified exponential distribution is a good fit. You can specify the SCALE= option as an alias for the SIGMA= option and the THRESHOLD= option as an alias for the THETA= option.

creates a gamma P-P plot. To create the plot, the nonmissing observations are ordered from smallest to largest:

The -coordinate of the th point is the empirical cdf value . The -coordinate is the theoretical gamma cdf value

where is the normalized incomplete gamma function, and

threshold parameter
scale parameter
shape parameter

You can specify , , and with the ALPHA=, SIGMA=, and THETA= gamma-options, as illustrated in the following example:

proc capability data=measures;
   ppplot width / gamma(alpha=1 sigma=2 theta=3);
run;

If you do not specify values for these parameters, then by default, and maximum likelihood estimates are calculated for and .

IMPORTANT: Your data must be greater than or equal to the lower threshold . If the default is not an adequate lower bound for your data, specify with the THETA= option.

If the data are gamma distributed with parameters , , and , the points on the plot for ALPHA=, SIGMA=, and THETA= tend to fall on or near the diagonal line , which is displayed by default. Agreement between the diagonal line and the point pattern is evidence that the specified gamma distribution is a good fit. You can specify the SHAPE= option as an alias for the ALPHA= option, the SCALE= option as an alias for the SIGMA= option, and the THRESHOLD= option as an alias for the THETA= option.

creates a lognormal P-P plot. To create the plot, the nonmissing observations are ordered from smallest to largest:

The -coordinate of the th point is the empirical cdf value . The -coordinate is the theoretical lognormal cdf value

where is the cumulative standard normal distribution function, and

threshold parameter
scale parameter
shape parameter

You can specify , , and with the THETA=, ZETA=, and SIGMA= lognormal-options, as illustrated in the following example:

proc capability data=measures;
   ppplot width / lognormal(theta=1 zeta=2);
run;

If you do not specify values for these parameters, then by default, and maximum likelihood estimates are calculated for and .

IMPORTANT: Your data must be greater than the lower threshold . If the default is not an adequate lower bound for your data, specify with the THETA= option.

If the data are lognormally distributed with parameters , , and , the points on the plot for SIGMA=, THETA=, and ZETA= tend to fall on or near the diagonal line , which is displayed by default. Agreement between the diagonal line and the point pattern is evidence that the specified lognormal distribution is a good fit. You can specify the SHAPE= option as an alias for the SIGMA= option, the SCALE= option as an alias for the ZETA= option, and the THRESHOLD= option as an alias for the THETA= option.

specifies the mean for a normal P-P plot requested with the NORMAL option. For examples, see Figure 5.18.3, or Figure 5.18.4 and Figure 5.18.5. By default, the sample mean is used for .

suppresses the diagonal reference line.

[Line Printer] suppresses the legend that indicates the number of hidden observations.

creates a normal P-P plot. By default, if you do not specify a distribution option, the procedure displays a normal P-P plot. To create the plot, the nonmissing observations are ordered from smallest to largest:

The -coordinate of the th point is the empirical cdf value . The -coordinate is the theoretical normal cdf value

where is the cumulative standard normal distribution function, and

location parameter or mean
scale parameter or standard deviation

You can specify and with the MU= and SIGMA= normal-options, as illustrated in the following example:

proc capability data=measures;
   ppplot width / normal(mu=1 sigma=2);
run;

By default, the sample mean and sample standard deviation are used for and .

If the data are normally distributed with parameters and , the points on the plot for MU= and SIGMA= tend to fall on or near the diagonal line , which is displayed by default. Agreement between the diagonal line and the point pattern is evidence that the specified normal distribution is a good fit. For an example, see Figure 5.18.3.

[Line Printer] specifies the character used to plot the points in a line printer plot. The default is the plus sign ().

specifies the parameter , where . When used with the BETA, EXPONENTIAL, GAMMA, NORMAL, and WEIBULL options, the SIGMA= option specifies the scale parameter. When used with the LOGNORMAL option, the SIGMA= option specifies the shape parameter. For an example of the SIGMA= option used with the NORMAL option, see Figure 5.18.3.

displays the P-P plot in a square frame. The default is a rectangular frame. See Figure 5.18.3 for an example.

[Line Printer] specifies the character used for the diagonal reference line in line printer plots. The default character is the first letter of the distribution option keyword.

specifies the lower threshold parameter for plots requested with the BETA, EXPONENTIAL, GAMMA, LOGNORMAL, and WEIBULL options.

is an alias for the THETA= option.

creates a Weibull P-P plot. To create the plot, the nonmissing observations are ordered from smallest to largest:

The -coordinate of the th point is the empirical cdf value . The -coordinate is the theoretical Weibull cdf value

where

threshold parameter
scale parameter
shape parameter

You can specify , , and with the C=, SIGMA=, and THETA= Weibull-options, as illustrated in the following example:

proc capability data=measures;
   ppplot width / weibull(theta=1 sigma=2);
run;

If you do not specify values for these parameters, then by default and maximum likelihood estimates are calculated for and .

IMPORTANT: Your data must be greater than or equal to the lower threshold . If the default is not an adequate lower bound for your data, you should specify with the THETA= option.

If the data are Weibull distributed with parameters , , and , the points on the plot for C=, SIGMA=, and THETA= tend to fall on or near the diagonal line , which is displayed by default. Agreement between the diagonal line and the point pattern is evidence that the specified Weibull distribution is a good fit. You can specify the SHAPE= option as an alias for the C= option, the SCALE= option as an alias for the SIGMA= option, and the THRESHOLD= option as an alias for the THETA= option.

specifies a value for the scale parameter for lognormal P-P plots requested with the LOGNORMAL option.