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QQPLOT Statement |

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

**ALPHA=***value-list*|EST-
specifies values for a mandatory shape parameter for Q-Q 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 QQPLOT 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 Q-Q 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
example, the first QQPLOT 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; qqplot width / beta(alpha=2 beta=2); qqplot width / beta(alpha=2 3 beta=1 2); qqplot width / beta(alpha=2 to 3 beta=1 to 2 by 0.5); qqplot 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 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

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 with intercept and slope with the`where , and lower threshold parameter scale parameter first shape parameter second shape parameter`*beta-options*THETA= and SIGMA=.Alternatively, you can add a line corresponding to estimated values of and slope with the*beta-options*THETA=EST and SIGMA=EST. Specify these options in parentheses, as in the following example:proc capability data=measures; qqplot 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 Q-Q 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 distribution option.
**C=***value(-list)*|EST-
specifies the shape parameter
*c*(*c*>0) for Q-Q 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 an example, see Output 10.3.1. **CAXIS=***color***CAXES=***color*- [
*Graphics*]

specifies the color 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***CFR=***color*- [
*Graphics*]

specifies the color for shading the area enclosed by the axes and frame. This area is not shaded by default. **CHREF=***color***CH=***color*- [
*Graphics*]

specifies the color for reference lines requested with the option. The default is the first color in the device color list. **COLOR=***color*- [
*Graphics*]

specifies the color for a distribution reference line. Specify the COLOR= option in parentheses following a distribution option keyword. For an example, see Figure 10.3. The default is the fourth color in the device color list. **CPKREF**- [
*Graphics*]

draws reference lines extending from the intersections of the specification limits with the distribution reference line to the quantile axis in plots requested with the NORMAL option. Specify CPKREF in parentheses after the NORMAL option. You can use the CPKREF option with the CPKSCALE option for graphical estimation of the capability indices*CPU*,*CPL*, and*C*_{pk}, as illustrated in Output 10.4.1. **CPKSCALE**-
rescales the quantile axis in
*C*_{pk}units for plots requested with the NORMAL option. Specify CPKSCALE in parentheses after the NORMAL option. You can use the CPKSCALE option with the CPKREF option for graphical estimation of the capability indices*CPU*,*CPL*, and*C*_{pk}, as illustrated in Output 10.4.1. **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. In the absence of a GOPTIONS statement, the default color is the first color in the device color list. **CVREF=***color***CV=***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 Q-Q 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 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 the threshold parameter, and is the scale parameter .

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

proc capability data=measures; qqplot 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 Q-Q plot for each value of the shape
parameter given by the mandatory ALPHA= option
or its alias, the SHAPE= option.
The following example produces three probability plots:

proc capability data=measures; qqplot width / gamma(alpha=0.4 to 0.6 by 0.1); 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 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 with intercept and slope 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; qqplot 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.

**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 Example 10.3
for illustrations. Related options
include the HREFCHAR=, CHREF=, and LHREF=options.
**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.
**L=***linetype*- [
*Graphics*]

specifies the line type for a distribution reference line. Specify the L= option in parentheses following a distribution option keyword. 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.
**LHREF=***linetype***LH=***linetype*- [
*Graphics*]

specifies the line type for reference lines requested by the HREF=option. 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 Q-Q plot for each value of the shape
parameter given by the mandatory SIGMA= option
or its alias, the SHAPE= option.
For example,
proc capability data=measures; qqplot width/ lognormal(shape=1.5 2.5); 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 cumulative standard normal distribution,*n*is the number of nonmissing observations, and is the shape parameter of the lognormal distribution.

The 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`where threshold parameter scale parameter shape parameter`

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. For an illustration, see Example 10.2.

To assess the point pattern, you can add a diagonal distribution reference line corresponding to the threshold parameter and the scale parameter 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. This line has intercept and slope . Agreement between the line and the point pattern indicates that the lognormal distribution with parameters , , and is a good fit. See Output 10.2.4 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. You can also display the reference line by specifying THETA=, and you can specify the slope with the SLOPE= option. For example, the following two QQPLOT statements produce charts with identical reference lines:proc capability data=measures; qqplot width / lognormal(sigma=2 theta=3 zeta=1); qqplot width / lognormal(sigma=2 theta=3 slope=2.718); run;

**LVREF=***linetype***LV=***linetype*- [
*Graphics*]

specifies the line type for reference lines requested by the VREF= option. The default is 2, which produces a dashed line. **MU=***value*|EST-
specifies a value for the mean for a normal Q-Q plot
requested with the NORMAL option. Specify MU= and
SIGMA= to request a distribution reference line
with intercept and slope .Specify MU=EST
to request a distribution reference line with intercept
equal to the sample mean, as illustrated in
Figure 10.3.
**NADJ=***value*-
specifies the adjustment value added to the sample size in the
calculation of theoretical quantiles.
The default
is (1/4), as described 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. For an example,
see Output 10.4.1.
**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 Q-Q 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 pattern on the plot tends to be linear with intercept and slope if the data are normally distributed with the specific density function

where is the mean, and is the standard deviation .

To assess the point pattern, you can add a diagonal distribution reference line with intercept and slope 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. Specify these options in parentheses, as in the following example:_{0}proc capability data=measures; qqplot length / normal(mu=10 sigma=0.3); run;

For an example, see "Adding a Distribution Reference Line". Agreement between the reference line and the point pattern indicates that the normal distribution with parameters and is a good fit. You can specify MU=EST and SIGMA=EST to request a distribution reference line with the sample mean and sample standard deviation as the intercept and slope.

Other*normal-options*include CPKREF and CPKSCALE. The CPKREF option draws reference lines extending from the intersections of specification limits with the distribution reference line to the theoretical quantile axis. The CPKSCALE option rescales the theoretical quantile axis in*C*_{pk}units. You can use the CPKREF option with the CPKSCALE option for graphical estimation of the capability indices*CPU*,*CPL*, and*C*_{pk}, as illustrated in Output 10.4.1. **NOSPECLEGEND****NOSPECL**-
suppresses the legend for specification limit reference
lines. For an example, see
Figure 10.3.
**PCTLAXIS(***axis-options*)-
adds a nonlinear percentile axis along the frame of
the Q-Q plot opposite the theoretical quantile axis.
The added axis is identical to the axis for probability
plots produced with the PROBPLOT statement.
When using the PCTLAXIS option, you must specify
HREF=values in quantile units,
and you cannot use the NOFRAME option. You can specify
the following
*axis-options*:

GRID draws vertical grid lines at major percentiles GRIDCHAR=' *character*'specifies grid line plotting character on line printer LABEL=' *string*'specifies label for percentile axis LGRID= *linetype*specifies line type for grid See CAPQQ1 in the SAS/QC Sample Library

For example, the following statements display the plot in Figure 10.4:

title 'Normal Quantile-Quantile Plot for Hole Distance'; proc capability data=sheets noprint; qqplot distance / normal(mu=est sigma=est color=yellow w=2) pctlaxis(grid lgrid=35 label='Normal Percentiles') nolegend cframe = ligr; run;

**PCTLMINOR**-
requests minor tick marks for the percentile axis displayed when
you use the PCTLAXIS option. See the entry for the PCTLAXIS
option for an example.
**PCTLSCALE**-
requests scale labels for the theoretical quantile axis
in percentile units, resulting in a nonlinear axis scale.
Tick marks are drawn uniformly across the axis based on the
quantile scale. In all other respects, the plot
remains the same, and you must specify HREF=values
in quantile units. For a true
nonlinear axis, use the PCTLAXIS option or use the PROBPLOT
statement.
For example,
the following
statements display the plot in
Figure 10.5:
See CAPQQ1 in the SAS/QC Sample Library

title 'Normal Quantile-Quantile Plot for Hole Distance'; proc capability data=sheets noprint; spec lsl=9.5 usl=10.5 llsl=2 lusl=20 clsl=blue cusl=blue; qqplot distance / normal(mu=est sigma=est color=yellow cpkref w=2) pctlscale pctlaxis(grid lgrid=35) nolegend cframe = ligr; run;

**QQSYMBOL='***character*'- [
*Line Printer*]

specifies the character used to plot the Q-Q points 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 quantiles.
The default
is -(3/8), as described 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=) refer to the horizontal axis, and vertical axis options (such as VAXIS=) 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 distribution parameter ,where .
Alternatively, you can specify SIGMA=EST to request a
maximum likelihood estimate for .The use of the SIGMA= option depends on
the distribution option specified, as indicated by the
following table:
**Distribution Option****Use of the SIGMA= Option**BETA THETA= and SIGMA= request a distribution reference EXPONENTIAL line with intercept and slope . GAMMA WEIBULL LOGNORMAL SIGMA= requests *n*Q-Q plots with shape parameters . The SIGMA= option is mandatory.NORMAL MU= and SIGMA= request a distribution reference line with intercept and slope . SIGMA=EST requests a slope equal to the sample standard deviation. WEIBULL2 SIGMA= and C= *c*request a distribution reference line with intercept and slope [1/(_{0}*c*)]._{0}

For an example using SIGMA=EST, see Output 10.4.1. For an example of lognormal plots using the SIGMA= option, see Example 10.2. **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= option. Specifying the SLOPE= option is an alternative to specifying ZETA=, which requests a slope of .See Output 10.2.4 for an example.

When you use the SLOPE= option with the WEIBULL2 option, you must also specify a scale parameter value with the SIGMA= option. Specifying the SLOPE= option is an alternative to specifying C=*c*, which requests a slope of [1/(_{0}*c*)]._{0}

For example, the first and second QQPLOT statements that follow produce plots identical to those produced by the third and fourth QQPLOT statements:proc capability data=measures; qqplot width / lognormal(sigma=2 theta=0 zeta=0); qqplot width / weibull2(sigma=2 theta=0 c=0.25); qqplot width / lognormal(sigma=2 theta=0 slope=1); qqplot width / weibull2(sigma=2 theta=0 slope=4); run;

For more information, see "Graphical Estimation". **SQUARE**-
displays the Q-Q plot in a square frame. Compare
Figure 10.1 with Figure 10.3.
The default is a rectangular frame.
**SYMBOL='***character*'- [
*Line Printer*]

specifies the character used to plot a distribution reference line when the plot is produced on a line printer. The default character is the first letter of the distribution option keyword.

**THETA=***value*|EST-
specifies the lower threshold parameter for
Q-Q 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. See Output 10.3.2 for an example.

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 10.2.4 for an example of the THETA= option with a lognormal Q-Q plot.

**THRESHOLD=***value*|EST-
is an alias for the THETA= option.

**VAXIS=***name*- [
*Graphics*]

specifies the name of an AXIS statement describing the vertical axis. For an example, see Example 10.1.

**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. For illustrations, see
Output 10.2.4 or Example 10.3.
Related options include the VREFCHAR=,
CVREF=, and LVREF= options.
**VREFCHAR='***character*'- [
*Line Printer*]

specifies the character used to form the reference 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 reference 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 distribution reference line, as in the following example. The default is 1.

proc capability data=measures; qqplot length / normal(mu=5 sigma=2 w=2); run;

**WEIBULL(C=***value-list*|EST <*Weibull-options*>)**WEIB(C=***value-list*<*Weibull-options*>)-
creates a three-parameter Weibull Q-Q plot for each value
of the shape parameter
*c*given by the mandatory C= option or its alias, the SHAPE= option. For example,proc capability data=measures; qqplot width / weibull(c=1.8 to 2.4 by 0.2); 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 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*c*is the 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. For an illustration, see Example 10.3. To assess the point pattern, you can add a diagonal distribution reference line with intercept and slope 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; qqplot 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 Q-Q plot. You should use
the WEIBULL2 option when your data have a
*known*lower threshold . You can specify the threshold value with the THETA= option or its alias, the THRESHOLD= option. If you are uncertain of the lower threshold value, you can estimate graphically by specifying a list of values for the THETA= option. Select the value that most linearizes the point pattern. 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)}, ,is plotted against the quantile log(-log(1-[(*i*- 0.375)/(*n*+ 0.25)] ) ), where*n*is the number of nonmissing observations. Unlike the three-parameter Weibull quantile, the preceding expression is free of distribution parameters. This is why the C= shape parameter option is not mandatory with the WEIBULL2 option.

The 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*c*is a shape parameter (*c*>0).

The advantage of a two-parameter Weibull plot over a three-parameter Weibull plot is that you can visually estimate the shape parameter*c*and the scale parameter from the slope and intercept of the point pattern; see Example 10.3 for an illustration of this method. The disadvantage is that the two-parameter Weibull distribution applies only in situations where the threshold parameter is known. See "Graphical Estimation" for more information.

To assess the point pattern, you can add a diagonal distribution reference line corresponding to the scale parameter and shape parameter*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. This line has intercept and slope [1/(*c*)]. Agreement between the line and the point pattern indicates that the Weibull distribution with parameters_{0}*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}

You can also display the reference line by specifying SIGMA=, and you can specify the slope with the SLOPE= option. For example, the following QQPLOT statements produce identical plots:proc capability data=measures; qqplot width / weibull2(theta=3 sigma=4 c=2); qqplot width / weibull2(theta=3 sigma=4 slope=0.5); run;

**ZETA=***value*|EST-
specifies a value for the scale parameter for lognormal
Q-Q plots requested with the LOGNORMAL option. Specify
THETA= and ZETA= to request a distribution
reference line with intercept and slope
.

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