Dictionary of Options

CDFPLOT Statement

Dictionary of Options

The following entries provide detailed descriptions of the options in the CDFPLOT statement.

ALPHA=value

specifies the shape parameter $\alpha$ for distribution functions requested with the BETA and GAMMA options. Enclose the ALPHA= option in parentheses after the BETA or GAMMA keywords. If you do not specify a value for $\alpha$ ,the procedure calculates a maximum likelihood estimate. For examples, see the entries for the BETA and GAMMA options.

ALPHADELTA=value

specifies the change in successive estimates of $\hat{\alpha}$ at which iteration terminates in the Newton-Raphson approximation of the maximum likelihood estimate of $\alpha$ for curves requested by the GAMMA option. Enclose the ALPHADELTA= option in parentheses after the GAMMA keyword. Iteration continues until the change in $\alpha$ is less than the value specified or the number of iterations exceeds the value of the MAXITER= option. The default value is 0.00001.

ALPHAINITIAL=value

specifies the initial value for $\hat{\alpha}$ in the Newton-Raphson approximation of the maximum likelihood estimate of $\alpha$ for fitted gamma distributions requested with the GAMMA option. Enclose the ALPHAINITIAL= option in parentheses after the GAMMA keyword. The default value is Thom's approximation of the estimate of $\alpha$ (refer to Johnson et al. (1995).

ANNOTATE=SAS-data-set

ANNO=SAS-data-set

[Graphics]
specifies an annotate data set, as described in SAS/GRAPH Software: Reference, that allows you to add features to the cdf plot. The ANNOTATE= data set you specify in the CDFPLOT statement is used for all plots created by the statement. You can also specify an ANNOTATE= data set in the PROC CAPABILITY statement, which provides annotate information used for all plots created by the procedure (see "ANNOTATE= Data Sets" ).

BETA<(beta-options )>

displays a fitted beta distribution function on the cdf plot. The equation of the fitted cdf is

$F(x) = \{ 0 & {for x \leq \theta} \ I_{\frac{x - \theta}{\sigma}} (\alpha , \beta ) & {for \theta \lt x \lt \theta + \sigma} \ 1 & {for x \geq \sigma + \theta} .$


where  is the incomplete beta function, and 
 
		  lower threshold parameter (lower endpoint)
		  scale parameter  
		  shape parameter  
		  shape parameter

The beta distribution is bounded below by the parameter $\theta$ and above by the value $\theta + \sigma$ .You can specify $\theta$ and $\sigma$ using the THETA= and SIGMA= beta-options, as illustrated in the following statements, which fit a beta distribution bounded between 50 and 75. The default values for $\theta$ and $\sigma$ are 0 and 1, respectively.

   proc capability;
      cdfplot / beta(theta=50 sigma=25);
   run;

The beta distribution has two shape parameters, $\alpha$ and $\beta$ . If these parameters are known, you can specify their values with the ALPHA= and BETA= beta-options. If you do not specify values for $\alpha$ and $\beta$ , the procedure calculates maximum likelihood estimates.

The BETA option can appear only once in a CDFPLOT statement. Table 2.2 and Table 2.3 list options you can specify with the BETA distribution option.

BETA=value

B=value

specifies the second shape parameter $\beta$ for beta distribution functions requested by the BETA option. Enclose the BETA= option in parentheses after the BETA keyword. If you do not specify a value for $\beta$ , the procedure calculates a maximum likelihood estimate. For examples, see the preceding entry for the BETA option.

C=value

specifies the shape parameter c for Weibull distribution functions requested with the WEIBULL option. Enclose the C= option in parentheses after the WEIBULL keyword. If you do not specify a value for c, the procedure calculates a maximum likelihood estimate. You can specify the SHAPE= option as an alias for the C= option.

CAXIS=color

CAXES=color

[Graphics]
specifies the color used for the axes and tick marks. This option overrides any COLOR= specifications in an AXIS statement. The default is the first color in the device color list.

CDELTA=value

specifies the change in successive estimates of c at which iterations terminate in the Newton-Raphson approximation of the maximum likelihood estimate of c for fitted Weibull curves requested by the WEIBULL option. Enclose the CDELTA= option in parentheses after the WEIBULL keyword. Iteration continues until the change in c between consecutive steps is less than the value specified or until the number of iterations exceeds the value of the MAXITER= option. The default value is 0.00001.

CDFSYMBOL='character'

[Line Printer]
specifies the character used to plot the points when the cdf plot is produced on a line printer. The default is the plus sign (+). Use the SYMBOL statement to control the plotting symbol when the plot is produced on a graphics device.

CFRAME=color

CFR=color

[Graphics]
specifies the color for the area enclosed by the axes and frame. This area is not shaded by default.

CHREF=color

CH=color

[Graphics]
specifies the color for lines requested by the HREF=option. The default is the first color in the device color list.

CINITIAL=value

specifies the initial value for $\hat{c}$ in the Newton-Raphson approximation of the maximum likelihood estimate of c for Weibull distributions requested by the WEIBULL option. The default value is 1.8 (refer to Johnson et al. 1995).

COLOR=color

[Graphics]
specifies the color of the fitted distribution curve. Enclose the COLOR= option in parentheses after a distribution option. .

CTEXT=color

[Graphics]
specifies the color for tick mark values and axis labels. The default is the color specified for the CTEXT= option in the most recent GOPTIONS statement.

CVREF=color

CV=color

[Graphics]
specifies the color for lines requested by the VREF= option. The default is the first color in the device color list.

DESCRIPTION='string'

DES='string'

[Graphics]
specifies a description, up to 40 characters, that appears in the PROC GREPLAY master menu. The default is the variable name.

EXPONENTIAL<(exponential-options )>

EXP<(exponential-options )>

displays a fitted exponential distribution function on the cdf plot. The equation of the fitted cdf is

$F(x) = \{ 0 & {for x \leq \theta} \ 1 - \exp (-\frac{x - \theta}{\sigma} ) & {for x \gt \theta\space } .$

where


		  threshold parameter
		  scale parameter

The parameter $\theta$ must be less than or equal to the minimum data value. You can specify $\theta$ with the THETA= exponential-option. The default value for $\theta$ is 0. You can specify $\sigma$ with the SIGMA= exponential-option. By default, a maximum likelihood estimate is computed for $\sigma$ . For example, the following statements fit an exponential distribution with $\theta = 10$ and a maximum likelihood estimate for $\sigma$ :

   proc capability;
      cdfplot / exponential(theta=10 l=2 color=green);
   run;

The exponential curve is green and has a line type of 2.

The EXPONENTIAL option can appear only once in a CDFPLOT statement. Table 2.2 and Table 2.4 list the options you can specify with the EXPONENTIAL option.

FONT=font

[Graphics]
specifies a software font for reference line and axis labels. You can also specify fonts for axis labels in an AXIS statement. The FONT= font takes precedence over the FTEXT= font specified in the most recent GOPTIONS statement. Hardware characters are used by default.

GAMMA<(gamma-options)>

displays a fitted gamma distribution function on the cdf plot. The equation of the fitted cdf is

$F(x) = \{ 0 & {for x \leq \theta} \ \frac{1}{\Gamma(\alpha) \sigma} \int_{\thet... ...pha - 1} \exp ( -\frac{t - \theta}{\sigma} ) dt & {for x \gt \theta\space } .$


where 
 
		  threshold parameter
		  scale parameter  
		  shape parameter

The parameter $\theta$ for the gamma distribution must be less than the minimum data value. You can specify $\theta$ with the THETA= gamma-option. The default value for $\theta$ is 0. In addition, the gamma distribution has a shape parameter $\alpha$ and a scale parameter $\sigma$ . You can specify these parameters with the ALPHA= and SIGMA= gamma-options. By default, maximum likelihood estimates are computed for $\alpha$ and $\sigma$ . For example, the following statements fit a gamma distribution function with $\theta=4$ and maximum likelihood estimates for $\alpha$ and $\sigma$ :

   proc capability;
      cdfplot / gamma(theta=4);
   run;

Note that the maximum likelihood estimate of $\alpha$ is calculated iteratively using the Newton-Raphson approximation. The gamma-options ALPHADELTA=, ALPHAINITIAL=, and MAXITER= control the approximation.

The GAMMA option can appear only once in a CDFPLOT statement. Table 2.2 and Table 2.5 list the options you can specify with the GAMMA option.

HAXIS=name

[Graphics]
specifies the name of an AXIS statement describing the horizontal axis.

HMINOR=n

HM=n

[Graphics]
specifies the number of minor tick marks between each major tick mark on the horizontal axis. Minor tick marks are not labeled. The default is 0.

HREF=value-list

draws reference lines perpendicular to the horizontal axis at the values specified. See Output 2.2.1 for an example that uses the similar VREF= option. See also the entries for the CHREF=, HREFCHAR=, and LHREF=options.

HREFCHAR='character'

[Line Printer]
specifies the character used to form the lines requested by the HREF=option. The default is the vertical bar (|).

HREFLABELS='label1' ... 'labeln'

HREFLABEL='label1' ... 'labeln'

HREFLAB='label1' ... 'labeln'

specifies labels for the lines requested by the HREF=option. The number of labels must equal the number of lines. Enclose each label in quotes. Labels can be up to 16 characters. See Output 2.2.1 for an example that uses the similar VREFLABELS= option.

LEGEND=name | NONE

[Graphics]
specifies the name of a LEGEND statement describing the legend for specification limit reference lines and superimposed distribution functions. Specifying LEGEND=NONE, which suppresses all legend information, is equivalent to specifying the NOLEGEND option.

LHREF=linetype

LH=linetype

[Graphics]
specifies the line type for lines requested by the HREF=option. The default is 2, which produces a dashed line.

LOGNORMAL<(lognormal-options)>

displays a fitted lognormal distribution function on the cdf plot. The equation of the fitted cdf is

$F(x) = \{ 0 & {for x \leq \theta} \ \Phi ( \frac{\log(x-\theta)-\zeta}{\sigma} ) & {for x \gt \theta\space } .$


where  is the standard normal cumulativedistribution function, and 
 
		  threshold parameter
		  scale parameter
		  shape parameter

The parameter $\theta$ for the lognormal distribution must be less than the minimum data value. You can specify $\theta$ with the THETA= lognormal-option. The default value for $\theta$ is 0. In addition, the lognormal distribution has a shape parameter $\sigma$ and a scale parameter $\zeta$ .You can specify these parameters with the SIGMA= and ZETA= lognormal-options. By default, maximum likelihood estimates are computed for $\sigma$ and $\zeta$ .For example, the following statements fit a lognormal distribution function with $\theta = 10$ and maximum likelihood estimates for $\sigma$ and $\zeta$ :

   proc capability;
      cdfplot / lognormal(theta = 10);
   run;

The LOGNORMAL option can appear only once in a CDFPLOT statement. Table 2.2 and Table 2.6 list options that you can specify with the LOGNORMAL option.

LVREF=linetype

LV=linetype

[Graphics]
specifies the line type for lines requested by the VREF= option. The default is 2, which produces a dashed line.

MAXITER=n

specifies the maximum number of iterations in the Newton-Raphson approximation of the maximum likelihood estimate of $\alpha$ for fitted gamma distributions requested with the GAMMA option and c for fitted Weibull distributions requested with the WEIBULL option. Enclose the MAXITER= option in parentheses after the GAMMA or WEIBULL keywords. The default value of n is 20.

MU=value

specifies the parameter $\mu$ for normal distribution functions requested with the NORMAL option. Enclose the MU= option in parentheses after the NORMAL keyword. The default value is the sample mean. For an example, see the entry for the NORMAL option.

NAME='string'

[Graphics]
specifies a name for the plot, up to eight characters, that appears in the PROC GREPLAY master menu. The default is 'CAPABILI'.

NOCDFLEGEND

suppresses the legend for the superimposed theoretical cumulative distribution function.

NOECDF

suppresses the observed distribution function (the empirical cumulative distribution function) of the variable, which is drawn by default. This option allows you to create theoretical cdf plots without displaying the data distribution. The NOECDF option can be used only with a theoretical distribution (such as the NORMAL option).

NOFRAME

suppresses the frame around the subplot area.

NOLEGEND

suppresses legends for specification limits, theoretical distribution functions, and hidden observations. Specifying the NOLEGEND option is equivalent to specifying LEGEND=NONE.

NORMAL<(normal-options)>

displays a fitted normal distribution function on the cdf plot. The equation of the fitted cdf is

$F(x) = .\Phi ( \frac{x - \mu}{\sigma} ) & {for -\infty \lt x \lt \infty} .$


where  is the standard normal cumulativedistribution function, and 
 
		  mean
		  standard deviation

You can specify known values for $\mu$ and $\sigma$ with the MU= and SIGMA= normal-options, as shown in the following statements:

   proc capability;
      cdfplot / normal(mu=14 sigma=.05);
   run;

By default, the sample mean and sample standard deviation are calculated for $\mu$ and $\sigma$ . The NORMAL option can appear only once in a CDFPLOT statement. For an example, see Output 2.1.1. Table 2.2 and Table 2.7 list options that you can specify with the NORMAL option.

NOSPECLEGEND

NOSPECL

suppresses the portion of the legend for specification limit reference lines.

SCALE=value

is an alias for the SIGMA= option for distributions requested by the BETA, EXPONENTIAL, GAMMA, and WEIBULL options and for the ZETA= option for distributions requested by the LOGNORMAL option.

SHAPE=value

is an alias for the ALPHA= option for distributions requested by the GAMMA option, for the SIGMA= option for distributions requested by the LOGNORMAL option, and for the C= option for distributions requested by the WEIBULL option.

SIGMA=value

specifies the parameter $\sigma$ for distribution functions requested by the BETA, EXPONENTIAL, GAMMA, LOGNORMAL, NORMAL, and WEIBULL options. Enclose the SIGMA= option in parentheses after the distribution keyword. The following table summarizes the use of the SIGMA= option:

Distribution Option	SIGMA= Specifies	Default Value	Alias
BETA	scale parameter $\sigma$	1	SCALE=
EXPONENTIAL	scale parameter $\sigma$	maximum likelihood estimate	SCALE=
GAMMA
WEIBULL
LOGNORMAL	shape parameter $\sigma$	maximum likelihood estimate	SHAPE=
NORMAL	scale parameter $\sigma$	standard deviation

SYMBOL='character'

[Line Printer]
specifies the character used to plot the theoretical distribution function if the cdf plot is produced on a line printer. Enclose the SYMBOL= option in parentheses after the distribution option. The default character is the first letter of the distribution option keyword.

THETA=value

specifies the lower threshold parameter $\theta$ for theoretical cumulative distribution functions requested with the BETA, EXPONENTIAL, GAMMA, LOGNORMAL, and WEIBULL options. Enclose the THETA= option in parentheses after the distribution keyword. The default value is 0.

THRESHOLD=value

is an alias for the THETA= option. See the preceding entry for the THETA= option.

VAXIS=name

[Graphics]
specifies the name of an AXIS statement describing the vertical axis. See Output 2.1.1 for an example.

VMINOR=n

VM=n

[Graphics]
specifies the number of minor tick marks between each major tick mark on the vertical axis. Minor tick marks are not labeled. The default is 0.

VREF=value-list

draws reference lines perpendicular to the vertical axis at the values specified. See Output 2.2.1 for an example. See also the entries for the CVREF=, LVREF=, and VREFCHAR= options.

VREFCHAR='character'

[Line Printer]
specifies the character used to form the lines requested by the VREF= option for a line printer. The default is the hyphen (-).

VREFLABELS='label1' ... 'labeln'

VREFLABEL='label1' ... 'labeln'

VREFLAB='label1' ... 'labeln'

specifies labels for the lines requested by the VREF= option. The number of labels must equal the number of lines. Enclose each label in quotes. Labels can be up to 16 characters. See Output 2.2.1 for an example.

VSCALE=PERCENT | PROPORTION

specifies the scale of the vertical axis. The value PERCENT scales the data in units of percent of observations per data unit. The value PROPORTION scales the data in units of proportion of observations per data unit. The default is PERCENT.

W=n

[Graphics]
specifies the width in pixels of the superimposed theoretical distribution. Enclose the W= option in parentheses after the distribution option. For example, the following statements display an exponential distribution with a width of 3. The default is 1.

   proc capability;
      cdfplot / exponential(w=3);
   run;

WEIBULL<(Weibull-options)>

displays a fitted Weibull distribution function on the cdf plot. The equation of the fitted cdf is

$F(x) = \{ 0 & {for x \leq \theta} \ 1 - \exp ( - ( \frac{x - \theta}{\sigma} )^c ) & {for x \gt \theta\space } .$


where 
 
		  threshold parameter
		  scale parameter  
		 c = shape parameter (c >0)

The parameter $\theta$ must be less than the minimum data value. You can specify $\theta$ with the THETA= Weibull-option. The default value for $\theta$ is 0. In addition, the Weibull distribution has a shape parameter c and a scale parameter $\sigma$ .You can specify these parameters with the SIGMA= and C= Weibull-options. By default, maximum likelihood estimates are computed for c and $\sigma$ .For example, the following statements fit a Weibull distribution function with $\theta=15$ and maximum likelihood estimates for $\sigma$ and c:

   proc capability;
      cdfplot / weibull(theta=15);
   run;

Note that the maximum likelihood estimate of c is calculated iteratively using the Newton-Raphson approximation. The Weibull-options CDELTA=, CINITIAL=, and MAXITER= control the approximation.

The WEIBULL option can appear only once in a CDFPLOT statement. Table 2.2 and Table 2.8 list options that you can specify with the WEIBULL option.

ZETA=value

specifies a value for the scale parameter $\zeta$ for a lognormal distribution function requested with the LOGNORMAL option. Enclose the ZETA= option in parentheses after the LOGNORMAL keyword. If you do not specify a value for $\zeta$ , a maximum likelihood estimate is computed. You can specify the SCALE= option as an alias for the ZETA= option.

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