Dictionary of Options

PROBPLOT Statement

Dictionary of Options

The following entries provide detailed descriptions of options for the PROBPLOT statement.

ALPHA=value-list|EST

specifies values for a mandatory shape parameter $\alpha$ $(\alpha\gt)$ for probability plots requested with the BETA and GAMMA options. A plot is created for each value specified. For examples, see the entries for the BETA and GAMMA options. If you specify ALPHA=EST, a maximum likelihood estimate is computed for $\alpha$ .

ANNOTATE=SAS-data-set

ANNO=SAS-data-set

[Graphics]
specifies an input data set containing annotate variables as described in SAS/GRAPH Software: Reference. You can use this data set to add features to the plot. The ANNOTATE= data set specified in the PROBPLOT statement is used for all plots created by the statement. You can also specify an ANNOTATE= data set in the PROC CAPABILITY statement to enhance all plots created by the procedure; for more information, see "ANNOTATE= Data Sets".

BETA(ALPHA=value-list|EST BETA=value-list|EST <beta-options >)

creates a beta probability plot for each combination of the shape parameters $\alpha$ and $\beta$ given by the mandatory ALPHA= and BETA= options. If you specify ALPHA=EST and BETA=EST, a plot is created based on maximum likelihood estimates for $\alpha$ and $\beta$ .In the following examples, the first PROBPLOT statement produces one plot, the second statement produces four plots, the third statement produces six plots, and the fourth statement produces one plot:

   proc capability data=measures;
      probplot width / beta(alpha=2 beta=2);
      probplot width / beta(alpha=2 3 beta=1 2);
      probplot width / beta(alpha=2 to 3 beta=1 to 2 by 0.5);
      probplot width / beta(alpha=est beta=est);
   run;

To create the plot, the observations are ordered from smallest to largest, and the i^th ordered observation is plotted against the quantile $B_{ \alpha \beta }^{-1} ( \frac{ i - 0.375 }{ n + 0.25 } )$ ,where $B_{ \alpha \beta}^{-1} ( \cdot )$ is the inverse normalized incomplete beta function, n is the number of nonmissing observations, and $\alpha$ and $\beta$ are the shape parameters of the beta distribution. The horizontal axis is scaled in percentile units.

The point pattern on the plot for ALPHA= $\alpha$ and BETA= $\beta$ tends to be linear with intercept^* $\theta$ and slope $\sigma$ if the data are beta distributed with the specific density function


		  
 
where  and 
 
		  lower threshold parameter
		  scale parameter  
		  first shape parameter  
		  second shape parameter

To obtain graphical estimates of $\alpha$ and $\beta$ ,specify lists of values for the ALPHA= and BETA= options, and select the combination of $\alpha$ and $\beta$ that most nearly linearizes the point pattern.

To assess the point pattern, you can add a diagonal distribution reference line corresponding to $\theta_0$ and $\sigma_0$ with the beta-options THETA= $\theta_0$ and SIGMA= $\sigma_0$ .Alternatively, you can add a line corresponding to estimated values of $\theta_0$ and $\sigma_0$ with the beta-options THETA=EST and SIGMA=EST. Specify these options in parentheses, as in the following example:

   proc capability data=measures;
      probplot width / beta(alpha=2 beta=3 theta=4 sigma=5);
   run;

Agreement between the reference line and the point pattern indicates that the beta distribution with parameters $\alpha$ , $\beta$ , $\theta_0$ and $\sigma_0$ 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.

BETA=value-list|EST

specifies values for the shape parameter $\beta$ $(\beta \gt)$ for probability plots requested with the BETA distribution option. A plot is created for each value specified with the BETA= option. If you specify BETA=EST, a maximum likelihood estimate is computed for $\beta$ .For examples, see the preceding entry for the BETA option.

C=value(-list)|EST

specifies the shape parameter c (c>0) for probability plots requested with the WEIBULL and WEIBULL2 options. You must specify C= as a Weibull-option with the WEIBULL option; in this situation it accepts a list of values, or if you specify C=EST, a maximum likelihood estimate is computed for c. You can optionally specify C=value or C=EST as a Weibull2-option with the WEIBULL2 option to request a distribution reference line; in this situation, you must also specify SIGMA=value or SIGMA=EST.

For example, the first PROBPLOT statement below creates three three-parameter Weibull plots corresponding to the shape parameters c=1, c=2, and c=3. The second PROBPLOT statement creates a single three-parameter Weibull plot corresponding to an estimated value of c. The third PROBPLOT statement creates a single two-parameter Weibull plot with a distribution reference line corresponding to c₀=2 and $\sigma_0=3$ .

   proc capability data=measures;
      probplot width / weibull(c=1 2 3);
      probplot width / weibull(c=est);
      probplot width / weibull2(c=2 sigma=3);
   run;

CAXIS=color

CAXES=color

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

CFRAME=color

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

CHREF=color

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

COLOR=color

[Graphics]
specifies the color for a diagonal distribution reference line. Specify the COLOR= option in parentheses following a distribution option keyword. The default is the first color in the device color list.

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

[Graphics]
specifies the color for reference 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 string is the variable name.

EXPONENTIAL<(exponential-options)>

EXP(<exponential-options>)

creates an exponential probability plot. To create the plot, the observations are ordered from smallest to largest, and the i^th ordered observation is plotted against the quantile -log (1-[(i-0.375)/(n+0.25)] ), where n is the number of nonmissing observations. The horizontal axis is scaled in percentile units.

The point pattern on the plot tends to be linear with intercept^* $\theta$ and slope $\sigma$ if the data are exponentially distributed with the specific density function

where $\theta$ is a threshold parameter, and $\sigma$ is a positive scale parameter.

To assess the point pattern, you can add a diagonal distribution reference line corresponding to $\theta_0$ and $\sigma_0$ with the exponential-options THETA= $\theta_0$ and SIGMA= $\sigma_0$ .Alternatively, you can add a line corresponding to estimated values of $\theta_0$ and $\sigma_0$ with the exponential-options THETA=EST and SIGMA=EST. Specify these options in parentheses, as in the following example:

   proc capability data=measures;
      probplot width / exponential(theta=4 sigma=5);
   run;

Agreement between the reference line and the point pattern indicates that the exponential distribution with parameters $\theta_0$ and $\sigma_0$ 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.

FONT=font

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

GAMMA(ALPHA=value-list|EST <gamma-options> )

creates a gamma probability plot for each value of the shape parameter $\alpha$ given by the mandatory ALPHA= option. If you specify ALPHA=EST, a plot is created based on a maximum likelihood estimate for $\alpha$ .

For example, the first PROBPLOT statement below creates three plots corresponding to $\alpha=0.4$ , $\alpha=0.5$ , and $\alpha=0.6$ .The second PROBPLOT statement creates a single plot.

   proc capability data=measures;
      probplot width / gamma(alpha=0.4 to 0.6 by 0.2);
      probplot width / gamma(alpha=est);
   run;

To create the plot, the observations are ordered from smallest to largest, and the i^th ordered observation is plotted against the quantile $G_{\alpha}^{-1} ( \frac{ i - 0.375 }{ n + 0.25 } )$ ,where $G_{\alpha}^{-1}(\cdot)$ is the inverse normalized incomplete gamma function, n is the number of nonmissing observations, and $\alpha$ is the shape parameter of the gamma distribution. The horizontal axis is scaled in percentile units.

The point pattern on the plot for ALPHA= $\alpha$ tends to be linear with intercept^* $\theta$ and slope $\sigma$ if the data are gamma distributed with the specific density function


		 
 
where 
 
		  threshold parameter
		  scale parameter  
		  shape parameter

To obtain a graphical estimate of $\alpha$ ,specify a list of values for the ALPHA= option, and select the value that most nearly linearizes the point pattern.

To assess the point pattern, you can add a diagonal distribution reference line corresponding to $\theta_0$ and $\sigma_0$ with the gamma-options THETA= $\theta_0$ and SIGMA= $\sigma_0$ .Alternatively, you can add a line corresponding to estimated values of $\theta_0$ and $\sigma_0$ with the gamma-options THETA=EST and SIGMA=EST. Specify these options in parentheses, as in the following example:

   proc capability data=measures;
      probplot width / gamma(alpha=2 theta=3 sigma=4);
   run;

Agreement between the reference line and the point pattern indicates that the gamma distribution with parameters $\alpha$ , $\theta_0$ and $\sigma_0$ 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.

GRID

draws reference lines perpendicular to the percentile axis at major tick marks.

GRIDCHAR='character'

[Line Printer]
specifies the character used to form the lines requested by the GRID option for a line printer. The default is the vertical bar (|).

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. For an example, see Output 9.2.1.

HREFCHAR='character'

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

HREFLABELS='label1' ... 'labeln'

HREFLABEL='label1' ... 'labeln'

HREFLAB='label1' ... 'labeln'

specifies labels for the reference 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. For an example, see Output 9.2.1.

L=linetype

[Graphics]
specifies the line type for a diagonal distribution reference line. Specify the L= option in parentheses after a distribution option keyword, as illustrated in the entry for the LOGNORMAL option. The default is 1, which produces a solid line.

LEGEND=name | NONE

specifies the name of a LEGEND statement describing the legend for specification limit reference lines and fitted curves. Specifying LEGEND=NONE is equivalent to specifying the NOLEGEND option.

LGRID=linetype

[Graphics]
specifies the line type for the reference lines requested by the GRID option. The default is 1, which produces solid lines.

LHREF=linetype

LH=linetype

[Graphics]
specifies the line type for reference lines requested by the HREF=option. For an example, see Output 9.2.1. The default is 2, which produces a dashed line.

LOGNORMAL(SIGMA=value-list|EST <lognormal-options >)

LNORM(SIGMA=value-list|EST <lognormal-options >)

creates a lognormal probability plot for each value of the shape parameter $\sigma$ given by the mandatory SIGMA= option or its alias, the SHAPE= option. If you specify SIGMA=EST, a plot is created based on a maximum likelihood estimate for $\sigma$ .

For example, the first PROBPLOT statement below produces two plots, and the second PROBPLOT statement produces a single plot:

   proc capability data=measures;
      probplot width / lognormal(sigma=1.5 2.5 l=2);
      probplot width / lognormal(sigma=est);
   run;

To create the plot, the observations are ordered from smallest to largest, and the i^th ordered observation is plotted against the quantile $\exp \!\! ( \sigma \Phi ^{-1} \! ( \frac{ i - 0.375 }{ n + 0.25 } ) )$ , where $\Phi^{-1}(\cdot)$ is the inverse standard cumulative normal distribution, n is the number of nonmissing observations, and $\sigma$ is the shape parameter of the lognormal distribution. The horizontal axis is scaled in percentile units.

The point pattern on the plot for SIGMA= $\sigma$ tends to be linear with intercept^* $\theta$ and slope $\exp(\zeta)$ if the data are lognormally distributed with the specific density function


		 
 
where 
 
		  threshold parameter
		  scale parameter
		  shape parameter

To obtain a graphical estimate of $\sigma$ ,specify a list of values for the SIGMA= option, and select the value that most nearly linearizes the point pattern.

To assess the point pattern, you can add a diagonal distribution reference line corresponding to $\theta_0$ and $\zeta_0$ with the lognormal-options THETA= $\theta_0$ and ZETA= $\zeta_0$ .Alternatively, you can add a line corresponding to estimated values of $\theta_0$ and $\zeta_0$ with the lognormal-options THETA=EST and ZETA=EST.

Specify these options in parentheses, as in the following example:

   proc capability data=measures;
      probplot width / lognormal(sigma=2 theta=3 zeta=0);
   run;

Agreement between the reference line and the point pattern indicates that the lognormal distribution with parameters $\sigma$ , $\theta_0$ , and $\zeta_0$ is a good fit. See Example 9.2 for an example.

You can specify the THRESHOLD= option as an alias for the THETA= option and the SCALE= option as an alias for the ZETA= option.

LVREF=linetype

[Graphics]
specifies the line type for reference lines requested by the VREF= option. For an example, see Output 9.2.1. The default is 2, which produces a dashed line.

MU=value|EST

specifies the mean $\mu_0$ for a normal probability plot requested with the NORMAL option. The MU= and SIGMA= normal-options must be specified together, and they request a distribution reference line as illustrated in Example 9.1. Specify MU=EST to request a distribution reference line with $\mu_0$ equal to the sample mean.

NADJ=value

specifies the adjustment value added to the sample size in the calculation of theoretical percentiles. The default is (1/4), as recommended by Blom (1958). Also refer to Chambers and others (1983) for additional information.

NAME='string'

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

NOFRAME

suppresses the frame around the area bounded by the axes.

NOLEGEND

LEGEND=NONE

suppresses legends for specification limits, fitted curves, distribution lines, and hidden observations.

NOLINELEGEND

NOLINEL

suppresses the legend for the optional distribution reference line.

NOOBSLEGEND

NOOBSL

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

NORMAL<(normal-options)>

NORM<(normal-options)>

creates a normal probability plot. This is the default if you do not specify a distribution option. To create the plot, the observations are ordered from smallest to largest, and the i^th ordered observation is plotted against the quantile $\Phi^{-1} \!\! ( \frac{i- 0.375}{n+ 0.25} )$ ,where $\Phi^{-1}(\cdot)$ is the inverse cumulative standard normal distribution, and n is the number of nonmissing observations. The horizontal axis is scaled in percentile units.

The point pattern on the plot tends to be linear with intercept^* $\mu$ and slope $\sigma$ if the data are normally distributed with the specific

where $\mu$ is the mean and $\sigma$ is the standard deviation ( $\sigma \gt 0$ ).

To assess the point pattern, you can add a diagonal distribution reference line corresponding to $\mu_0$ and $\sigma_0$ with the normal-options MU= $\mu_0$ and SIGMA= $\sigma_0$ .Alternatively, you can add a line corresponding to estimated values of $\mu_0$ and $\sigma_0$ with the normal-options THETA=EST and SIGMA=EST; the estimates of $\mu_0$ and ]sigma₀ are the sample mean and sample standard deviation.

Specify these options in parentheses, as in the following example:

   proc capability data=measures;
      probplot length / normal(mu=10 sigma=0.3);
      probplot length / normal(mu=est sigma=est);
   run;

Agreement between the reference line and the point pattern indicates that the normal distribution with parameters $\mu_0$ and $\sigma_0$ is a good fit.

NOSPECLEGEND

NOSPECL

suppresses the legend for specification limit reference lines.

PCTLMINOR

requests minor tick marks for the percentile axis. See Output 9.2.1 for an example.

PCTLORDER=value-list

specifies the tick mark values labeled on the theoretical percentile axis. Since the values are percentiles, the labels must be between 0 and 100, exclusive. The values must be listed in increasing order and must cover the plotted percentile range. Otherwise, a default list is used. For example, consider the following:

   proc capability data=measures;
      probplot length / pctlorder=1 10 25 50 75 90 99;
   run;

Note that the ORDER= option in the AXIS statement is not supported by the PROBPLOT statement.

PROBSYMBOL='character'

[Line Printer]
specifies the character used to mark the points when the plot is produced on a line printer. The default is the plus sign (+).

RANKADJ=value

specifies the adjustment value added to the ranks in the calculation of theoretical percentiles. The default is -(3/8), as recommended by Blom (1958). Also refer to Chambers and others (1983) for additional information.

ROTATE

[Graphics]
switches the horizontal and vertical axes so that the theoretical percentiles are plotted vertically while the data are plotted horizontally. Regardless of whether the plot has been rotated, horizontal axis options (such as HAXIS=) still refer to the horizontal axis, and vertical axis options (such as VAXIS=) still refer to the vertical axis. All other options that depend on axis placement adjust to the rotated axes.

SCALE=value|EST

is an alias for the SIGMA= option with the BETA, EXPONENTIAL, GAMMA, WEIBULL and WEIBULL2 options and for the ZETA= option with the LOGNORMAL option. See the entries for the SIGMA= and ZETA= options.

SHAPE=value-list|EST

is an alias for the ALPHA= option with the GAMMA option, for the SIGMA= option with the LOGNORMAL option, and for the C= option with the WEIBULL and WEIBULL2 options. See the entries for the ALPHA=, C=, and SIGMA= options.

SIGMA=value-list|EST

specifies the value of the parameter $\sigma$ , where $\sigma \gt 0$ . Alternatively, you can specify SIGMA=EST to request a maximum likelihood estimate for $\sigma_0$ .The interpretation and use of the SIGMA= option depend on the distribution option with which it is specified, as indicated by the following table:

Distribution Option	Use of the SIGMA= Option
BETA	THETA= $\theta_0$ and SIGMA= $\sigma_0$ request a distribution reference
EXPONENTIAL	line corresponding to $\theta_0$ and $\sigma_0$ .
GAMMA
WEIBULL
LOGNORMAL	SIGMA= $\sigma_1 ... \sigma_n$ requests n probability plots with shape parameters $\sigma_1 ... \sigma_n$ .The SIGMA= option must be specified.
NORMAL	MU= $\mu_0$ and SIGMA= $\sigma_0$ request a distribution reference line corresponding to $\mu_0$ and $\sigma_0$ .SIGMA=EST requests a line with $\sigma_0$ equal to the sample standard deviation.
WEIBULL2	SIGMA= $\sigma_0$ and C=c₀ request a distribution reference line corresponding to $\sigma_0$ and c₀.

In the following example, the first PROBPLOT statement requests a normal plot with a distribution reference line corresponding to $\mu_{0}=5$ and $\sigma_{0}=2$ ,and the second PROBPLOT statement requests a lognormal plot with shape parameter $\sigma=3$ :

   proc capability data=measures;
      probplot length / normal(mu=5 sigma=2);
      probplot width  / lognormal(sigma=3);
   run;

SLOPE=value|EST

specifies the slope^* for a distribution reference line requested with the LOGNORMAL and WEIBULL2 options.

When you use the SLOPE= option with the LOGNORMAL option, you must also specify a threshold parameter value $\theta_0$ with the THETA= lognormal-option to request the line. The SLOPE= option is an alternative to the ZETA= lognormal-option for specifying $\zeta_0$ , since the slope is equal to $\exp(\zeta_0)$ .

When you use the SLOPE= option with the WEIBULL2 option, you must also specify a scale parameter value $\sigma_0$ with the SIGMA= Weibull2-option to request the line. The SLOPE= option is an alternative to the C= Weibull2-option for specifying c₀, since the slope is equal to 1/c₀. See "Location and Scale Parameters".

For example, the first and second PROBPLOT statements below produce the same set of probability plots as the third and fourth PROBPLOT statements:

   proc capability data=measures;
      probplot width / lognormal(sigma=2 theta=0 zeta=0);
      probplot width / weibull2(sigma=2 theta=0 c=0.25);
      probplot width / lognormal(sigma=2 theta=0 slope=1);
      probplot width / weibull2(sigma=2 theta=0 slope=4);
   run;

SQUARE

displays the probability plot in a square frame. For an example, see Output 9.2.1. The default is a rectangular frame.

SYMBOL='character'

[Line Printer]
specifies the character used to display the distribution reference line when the plot is created using a line printer. The default character is the first letter of the distribution option keyword.

THETA=value|EST

specifies the lower threshold parameter $\theta$ for plots requested with the BETA, EXPONENTIAL, GAMMA, LOGNORMAL, WEIBULL, and WEIBULL2 options. When used with the WEIBULL2 option, the THETA= option specifies the known lower threshold $\theta_0$ , for which the default is 0. When used with the other distribution options, the THETA= option specifies $\theta_0$ for a distribution reference line; alternatively in this situation, you can specify THETA=EST to request a maximum likelihood estimate for $\theta_0$ .To request the line, you must also specify a scale parameter. See Output 9.2.1 for an example of the THETA= option with a lognormal probability plot.

THRESHOLD=value

is an alias for the THETA= option.

VAXIS=name

[Graphics]
specifies the name of an AXIS statement describing the vertical axis, as illustrated by Output 9.1.1.

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 9.2.1 for an example.

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.

W=n

[Graphics]
specifies the width in pixels for a diagonal distribution reference line. Specify the W= option in parentheses after a distribution option keyword. For an example, see the entry for the WEIBULL option. The default is 1.

WEIBULL(C=value-list|EST <Weibull-options >)

WEIB(C=value-list <Weibull-options >)

creates a three-parameter Weibull probability plot for each value of the shape parameter c given by the mandatory C= option or its alias, the SHAPE= option. If you specify C=EST, a plot is created based on a maximum likelihood estimate for c. In the following example, the first PROBPLOT statement creates four plots, and the second PROBPLOT statement creates a singlel plot:

   proc capability data=measures;
      probplot width / weibull(c=1.8 to 2.4 by 0.2 w=2);
      probplot width / weibull(c=est);
   run;

To create the plot, the observations are ordered from smallest to largest, and the i^th ordered observation is plotted against the quantile ( -log (1-[(i-0.375)/(n+0.25)] ) )^[1/c], where n is the number of nonmissing observations, and c is the Weibull distribution shape parameter. The horizontal axis is scaled in percentile units.

The point pattern on the plot for C=c tends to be linear with intercept^* $\theta$ and slope $\sigma$ if the data are Weibull distributed with the specific density function


		 
[.05in]where 
 
		  threshold parameter
		  scale parameter  
		 c = shape parameter ( c > 0 )

To obtain a graphical estimate of c, specify a list of values for the C= option, and select the value that most nearly linearizes the point pattern.

To assess the point pattern, you can add a diagonal distribution reference line corresponding to $\theta_0$ and $\sigma_0$ with the Weibull-options THETA= $\theta_0$ and SIGMA= $\sigma_0$ .Alternatively, you can add a line corresponding to estimated values of $\theta_0$ and $\sigma_0$ with the Weibull-options THETA=EST and SIGMA=EST. Specify these options in parentheses, as in the following example:

   proc capability data=measures;
      probplot width / weibull(c=2 theta=3 sigma=4);
   run;

Agreement between the reference line and the point pattern indicates that the Weibull distribution with parameters c, $\theta_0$ ,and $\sigma_0$ 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.

WEIBULL2<(Weibull2-options)>

W2<(Weibull2-options)>

creates a two-parameter Weibull probability plot. You should use the WEIBULL2 option when your data have a known lower threshold $\theta_0$ . You can specify the threshold value $\theta_0$ with the THETA= Weibull2-option or its alias, the THRESHOLD= Weibull2-option. The default is $\theta_0 = 0$ .

To create the plot, the observations are ordered from smallest to largest, and the log of the shifted i^th ordered observation x_(i), denoted by $\log(x_{(i)} - \theta_0 )$ ,is plotted against the quantile log (-log (1-[(i-0.375)/(n+0.25)] ) ), where n is the number of nonmissing observations. The horizontal axis is scaled in percentile units. Note that the C= shape parameter option is not mandatory with the WEIBULL2 option. The point pattern on the plot for THETA= $\theta_0$ tends to be linear with intercept $\log(\sigma)$ and slope [1/c] if the data are Weibull distributed with the specific density function


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

An advantage of the two-parameter Weibull plot over the three-parameter Weibull plot is that the parameters c and $\sigma$ can be estimated from the slope and intercept of the point pattern. A disadvantage is that the two-parameter Weibull distribution applies only in situations where the threshold parameter is known.

To assess the point pattern, you can add a diagonal distribution reference line corresponding to $\sigma_0$ and c₀ with the Weibull2-options SIGMA= $\sigma_0$ and C=c₀. Alternatively, you can add a distribution reference line corresponding to estimated values of $\sigma_0$ and c₀ with the Weibull2-options SIGMA=EST and C=EST. Specify these options in parentheses, as in the following example:

   proc capability data=measures;
      probplot width / weibull2(theta=3 sigma=4 c=2);
   run;

Agreement between the distribution reference line and the point pattern indicates that the Weibull distribution with parameters c₀, $\theta_0$ and $\sigma_0$ is a good fit. You can specify the SCALE= option as an alias for the SIGMA= option and the SHAPE= option as an alias for the C= option.

ZETA=value|EST

specifies a value for the scale parameter $\zeta$ for lognormal probability plots requested with the LOGNORMAL option. Specify THETA= $\theta_0$ and ZETA= $\zeta_0$ to request a distribution reference line with intercept $\theta_0$ and slope $\exp(\zeta_0)$ .See Output 9.2.1 for an example.

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