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PROBPLOT Statement |

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

**ALPHA=***value-list*|EST-
specifies values for a mandatory shape parameter 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 .
**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 and 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 and .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 ,where is the inverse normalized incomplete beta function,*n*is the number of nonmissing observations, and and are the shape parameters of the beta distribution. The horizontal axis is scaled in percentile units.

The point pattern on the plot for ALPHA= and BETA= tends to be linear with intercept^{*}and slope 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 and ,specify lists of values for the ALPHA= and BETA= options, and select the combination of and that most nearly linearizes the point pattern.

To assess the point pattern, you can add a diagonal distribution reference line corresponding to and with the*beta-options*THETA= and SIGMA=.Alternatively, you can add a line corresponding to estimated values of and 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 , , and 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 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 .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*c*=2 and ._{0}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^{*}and slope if the data are exponentially distributed with the specific density function

where is a threshold parameter, and is a positive scale parameter.

To assess the point pattern, you can add a diagonal distribution reference line corresponding to and with the*exponential-options*THETA= and SIGMA=.Alternatively, you can add a line corresponding to estimated values of and 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 and 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 given by the mandatory ALPHA=
option.
If you specify ALPHA=EST, a
plot is created based on a
maximum likelihood estimate
for .

For example, the first PROBPLOT statement below creates three plots corresponding to , , and .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 ,where is the inverse normalized incomplete gamma function,*n*is the number of nonmissing observations, and is the shape parameter of the gamma distribution. The horizontal axis is scaled in percentile units.

The point pattern on the plot for ALPHA= tends to be linear with intercept^{*}and slope if the data are gamma distributed with the specific density function

To obtain a graphical estimate of ,specify a list of values for the ALPHA= option, and select the value that most nearly linearizes the point pattern.`where threshold parameter scale parameter shape parameter`

To assess the point pattern, you can add a diagonal distribution reference line corresponding to and with the*gamma-options*THETA= and SIGMA=.Alternatively, you can add a line corresponding to estimated values of and 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 , and 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 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 .

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 , where is the inverse standard cumulative normal distribution,*n*is the number of nonmissing observations, and is the shape parameter of the lognormal distribution. The horizontal axis is scaled in percentile units.

The point pattern on the plot for SIGMA= tends to be linear with intercept^{*}and slope if the data are lognormally distributed with the specific density function

To obtain a graphical estimate of ,specify a list of values for the SIGMA= option, and select the value that most nearly linearizes the point pattern.`where threshold parameter scale parameter shape parameter`

To assess the point pattern, you can add a diagonal distribution reference line corresponding to and with the*lognormal-options*THETA= and ZETA=.Alternatively, you can add a line corresponding to estimated values of and 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 , , and 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 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 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 ,where 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^{*}and slope if the data are normally distributed with the specific

where is the mean and is the standard deviation ().

To assess the point pattern, you can add a diagonal distribution reference line corresponding to and with the*normal-options*MU= and SIGMA=.Alternatively, you can add a line corresponding to estimated values of and with the*normal-options*THETA=EST and SIGMA=EST; the estimates of and ]*sigma*are the sample mean and sample standard deviation._{0}

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 and 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
, where .
Alternatively, you can specify SIGMA=EST to request a
maximum likelihood estimate for .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= and SIGMA= request a distribution reference EXPONENTIAL line corresponding to and . GAMMA WEIBULL LOGNORMAL SIGMA= requests *n*probability plots with shape parameters .The SIGMA= option must be specified.NORMAL MU= and SIGMA= request a distribution reference line corresponding to and .SIGMA=EST requests a line with equal to the sample standard deviation. WEIBULL2 SIGMA= and C= *c*request a distribution reference line corresponding to and_{0}*c*._{0}

In the following example, the first PROBPLOT statement requests a normal plot with a distribution reference line corresponding to and ,and the second PROBPLOT statement requests a lognormal plot with shape parameter :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 with the THETA=*lognormal-option*to request the line. The SLOPE= option is an alternative to the ZETA=*lognormal-option*for specifying , since the slope is equal to .

When you use the SLOPE= option with the WEIBULL2 option, you must also specify a scale parameter value with the SIGMA=*Weibull2-option*to request the line. The SLOPE= option is an alternative to the C=*Weibull2-option*for specifying*c*, since the slope is equal to 1/_{0}*c*. See "Location and Scale Parameters"._{0}

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 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 , for which the default is 0.
When used with the
other distribution options,
the THETA= option specifies for a distribution
reference line;
alternatively in this situation, you can specify THETA=EST to request a
maximum likelihood estimate for .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^{*}and slope 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 and with the*Weibull-options*THETA= and SIGMA=.Alternatively, you can add a line corresponding to estimated values of and 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*, ,and 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 . You can specify the threshold value with the THETA=*Weibull2-option*or its alias, the THRESHOLD=*Weibull2-option*. The default is .

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 ,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= tends to be linear with intercept 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 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 and*c*with the_{0}*Weibull2-options*SIGMA= and C=*c*. Alternatively, you can add a distribution reference line corresponding to estimated values of and_{0}*c*with the_{0}*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*c*, and 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._{0} **ZETA=***value*|EST-
specifies a value for the scale parameter for lognormal
probability plots requested with the LOGNORMAL option. Specify
THETA= and ZETA= to request a distribution
reference line with intercept and slope
.See Output 9.2.1 for an example.

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Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.