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QQPLOT Statement

Alias:	QQ
Default:	Normal Q-Q plot
Restriction:	You can specify only one theoretical distribution.
Tip:	You can use multiple QQPLOT statements.
Main Discussion:	Quantile-Quantile and Probability Plots

To do this:		Use this option:
Request a distribution
	Specify beta probability plot with required shape parameters , .	BETA(beta-suboptions)
	Specify exponential probability plot	EXPONENTIAL(exponential-suboptions)
	Specify gamma probability plot with a required shape parameter	GAMMA(gamma-suboptions)
	Specify lognormal probability plot with a required shape parameter	LOGNORMAL(lognormal-suboptions)
	Specify normal probability plot	NORMAL(normal-suboptions)
	Specify three-parameter Weibull probability plot with a required shape parameter	WEIBULL(Weibull-suboptions)
	Specify two-parameter Weibull probability plot	WEIBULL2(Weibull2-suboptions)
Distribution suboptions
	Specify shape parameter for the beta or gamma distribution	ALPHA=
	Specify shape parameter for the beta distribution	BETA=
	Specify shape parameter for the Weibull distribution or for distribution reference line of the Weibull2 distribution	C=
	Specify for distribution reference line of the normal distribution	MU=
	Specify for distribution reference line for the beta, exponential, gamma, normal, Weibull, or Weibull2 distribution or the required shape parameter for the lognormal option	SIGMA=
	Specify slope of distribution reference line for the lognormal or Weibull2 distribution	SLOPE=
	Specify for distribution reference line for the beta, exponential, gamma. lognormal, or Weibull distribution, or the lower known threshold for the Weibull2 distribution	THETA=
	Specify for distribution reference line for the lognormal distribution	ZETA=
Control appearance of distribution reference line
	Specify color of distribution reference line	COLOR=
	Specify line type of distribution reference line	L=
	Specify width of distribution reference line	W=
Control general plot layout
	Specify reference lines perpendicular to the horizontal axis	HREF=
	Specify labels for HREF lines	HREFLABELS=
	Adjust sample size when computing quantiles	NADJ=
	Suppress frame around plotting area	NOFRAME
	Request minor tick marks for percentile axis	PCTLMINOR
	Replace theoretical quantiles with percentiles	PCTLSCALE
	Adjust ranks when computing quantiles	RANKADJ=
	Display Q-Q plot in square format	SQUARE
	Specify reference lines perpendicular to the vertical axis	VREF=
	Specify labels for VREF lines	VREFLABELS=
Enhance the Q-Q plot
	Specify annotate data set	ANNOTATE=
	Specify color for axis	CAXIS=
	Specify color for frame	CFRAME=
	Specify color for HREF= lines	CHREF=
	Specify color for text	CTEXT=
	Specify color for VREF= lines	CVREF=
	Specify description for plot in graphics catalog	DESCRIPTION=
	Specify software font for text	FONT=
	Specify number of minor tick marks on horizontal axis	HMINOR=
	Specify line style for HREF= lines	LHREF=
	Specify line style for VREF= lines	LVREF=
	Specify name for plot in graphics catalog	NAME=
	Specify number of minor tick marks on vertical axis	VMINOR=
Enhance the comparative Q-Q plot
	Apply annotation requested in ANNOTATE= data set to key cell only	ANNOKEY
	Specify color for filling frame for row labels	CFRAMESIDE=
	Specify color for filling frame for column labels	CFRAMETOP=
	Specify distance between tiles	INTERTILE=
	Specify number of columns in comparative Q-Q plot	NCOLS=
	Specify number of rows in comparative Q-Q plot	NROWS=

Arguments

variable(s)

identifies one or more variables that the procedure uses to create Q-Q plots.

Default:	If you omit variable(s) in the QQPLOT statement, then the procedure creates a Q-Q plot for each variable that you list in the VAR statement, or for each numeric variable in the DATA= data set if you omit a VAR statement.
Requirement:	If you specify a VAR statement, use the variable(s) that you list in the VAR statement. Otherwise, variable(s) are any numeric variables in the DATA= data set.

Options

ALPHA=value(s)|EST

specifies the required shape parameter for quantile plots when you request the BETA or GAMMA options. The QQPLOT statement creates a plot for each value that you specify.

Requirement:	Enclose this suboption in parentheses when it follows the BETA or GAMMA options.
Tip:	To compute a maximum likelihood estimate for , specify ALPHA=EST.

ANNOKEY

specifies to apply the annotation that you requested with the ANNOTATE= option to the key cell only. By default, PROC UNIVARIATE applies annotation to all of the cells.

Requirement:	This option is ignored unless you specify the CLASS statement.
Tip:	Use the KEYLEVEL= option in the CLASS statement to specify the key cell.
See also:	the KEYLEVEL= option

ANNOTATE=SAS-data-set

specifies an input data set that contains annotate variables as described in SAS/GRAPH Software: Reference.

Alias:	ANNO=
Tip:	The ANNOTATE = data set that you specify in the QQPLOT statement is used by all plots that this statement creates. You can also specify an ANNOTATE= data set in the PROC UNIVARIATE statement to enhance all the graphic displays that the procedure creates.
See also:	ANNOTATE= in the PROC UNIVARIATE statement

BETA(ALPHA=value(s)|EST BETA=value(s)|EST <beta-suboptions>)

displays a beta Q-Q plot for each combination of the required shape parameters and .

Requirement:	You must specify the shape parameters with the ALPHA= and BETA= suboptions
Interaction:	To create a plot that is based on maximum likelihood estimates for and , specify ALPHA=EST and BETA=EST.
Tip:	To obtain graphical estimates of and , specify lists of values in the ALPHA= and BETA= suboptions. Then select the combination of and that most nearly linearizes the point pattern. To assess the point pattern, add a diagonal distribution reference line that corresponds to the lower threshold parameter and the scale parameter with the THETA= and SIGMA= suboptions. Alternatively, you can add a line that corresponds to estimated values of lower threshold parameter and with THETA=EST and SIGMA=EST. Agreement between the reference line and the point pattern indicates that the beta distribution with parameters , , , and is a good fit.
Main discussion:	Beta Distribution
See also:	the ALPHA= suboption , BETA= suboption , SIGMA= suboption , and THETA= suboption .

BETA=value(s)|EST

specifies the shape parameter for Q-Q plots when you request the BETA distribution option. PROC UNIVARIATE creates a plot for each value that you specify.

Alias:	B=
Requirement:	You must enclose this suboption in parentheses after the BETA option.
Tip:	To compute a maximum likelihood estimate for , specify BETA=EST.

C=value(s)|EST

specifies the shape parameter for Q-Q plots when you request the WEIBULL option or WEIBULL2 option. C= is a required suboption in the WEIBULL option.

Requirement:	Enclose this suboption in parentheses after the WEIBULL option or WEIBULL2 option.
Interaction:	To request a distribution reference line in the WEIBULL2 option, you must specify both the C= and SIGMA= suboptions.
Tip:	To compute a maximum likelihood estimate for , specify C=EST.

CAXIS=color

specifies the color for the axes.

Alias:	CAXES=
Default:	the first color in the device color list
Interaction:	This option overrides any COLOR= specification.

CFRAME=color

specifies the color for the area that is enclosed by the axes and frame.

Default:

the area is not filled

CFRAMESIDE=color

specifies the color to fill the frame area for the row labels that display along the left side of the comparative probability plot. This color also fills the frame area for the label of the corresponding class variable (if you associate a label with the variable).

Default:	These areas are not filled.
Requirement:	This option is ignored unless you specify the CLASS statement.

CFRAMETOP=color

specifies the color to fill the frame area for the column labels that display across the top of the comparative probability plot. This color also fills the frame area for the label of the corresponding class variable (if you associate a label with the variable).

Default:	These areas are not filled.
Requirement:	This option is ignored unless you specify the CLASS statement.

CHREF=color

specifies the color for horizontal axis reference lines when you specify the HREF= option.

Default:

the first color in the device color list

COLOR=color

specifies the color for a distribution reference line.

Default:	the fourth color in the device color list
Requirement:	You must enclose this suboption in parentheses after a distribution option keyword.

CTEXT=color

specifies the color for tick mark values and axis labels.

Default:

the color that you specify for the CTEXT= option in the GOPTIONS statement. If you omit the GOPTIONS statement, the default is the first color in the device color list.

CVREF=color

specifies the color for the reference lines that you request with the VREF= option.

Alias:	CV=
Default:	the first color in the device color list.

DESCRIPTION='string'

specifies a description, up to 40 characters long, that appears in the PROC GREPLAY master menu.

Alias:	DES=
Default:	the variable name

EXPONENTIAL<(exponential-suboptions)>

displays an exponential Q-Q plot.

Alias:	EXP
Tip:	To assess the point pattern, add a diagonal distribution reference line that corresponds to and with the THETA= and SIGMA= suboptions. Alternatively, you can add a line that corresponds to estimated values of the threshold parameter and the scale parameter with the THETA=EST and SIGMA=EST suboptions. Agreement between the reference line and the point pattern indicates that the exponential distribution with parameters and is a good fit.
Main discussion:	Exponential Distribution
See also:	the SIGMA suboption and THETA suboption

FONT=font

specifies a software font for the reference lines and the axis labels.

Default:	hardware characters
Interaction:	FONT=font takes precedence over FTEXT=font that you specify in the GOPTIONS statement.

GAMMA(ALPHA=value(s)|EST <gamma-suboptions>)

displays a gamma Q-Q plot for each value of the required shape parameter .

Requirement:	You must specify the shape parameter with the ALPHA= suboption.
Interaction:	To create a plot that is based on a maximum likelihood estimate for , specify ALPHA=EST.
Tip:	To obtain a graphical estimate of , specify a list of values in the ALPHA= suboption. Then select the value that most nearly linearizes the point pattern. To assess the point pattern, add a diagonal distribution reference line that corresponds to and with the THETA= and SIGMA= suboptions. Alternatively, you can add a line that corresponds to estimated values of the threshold parameter and the scale parameter with THETA=EST and SIGMA=EST. Agreement between the reference line and the point pattern indicates that the exponential distribution with parameters , , and is a good fit.
Main discussion:	Gamma Distribution
See also:	the ALPHA= suboption , SIGMA= suboption , and THETA= suboption

HMINOR=n

specifies the number of minor tick marks between each major tick mark on the horizontal axis. PROC UNIVARIATE does not label minor tick marks.

Alias:	HM=
Default:	0

HREF=value(s)

draws reference lines that are perpendicular to the horizontal axis at the values you specify.

See also:

CHREF= option

HREFLABELS='label1' ... ' labeln'

specifies labels for the reference lines that you request with the HREF= option.

Alias:	HREFLABEL= and HREFLAB=
Restriction:	The number of labels must equal the number of reference lines. Labels can have up to 16 characters.

INTERTILE=value

specifies the distance in horizontal percentage screen units between the framed areas, which are called tiles.

Default:	The tiles are contiguous.
Requirement:	This option is ignored unless you specify the CLASS statement.

L=linetype

specifies the line type for a diagonal distribution reference line.

Default:	1, which produces a solid line
Requirement:	You must enclose this suboption in parentheses after a distribution option keyword.

LHREF=linetype

specifies the line type for the reference lines that you request with the HREF= option.

Alias:	LH=
Default:	2, which produces a dashed line

LOGNORMAL(SIGMA=value(s)|EST <lognormal-suboptions>)

displays a lognormal Q-Q plot for each value of the required shape parameter .

Alias:	LNORM
Requirement:	You must specify the shape parameter with the SIGMA= suboption.
Tip:	To obtain a graphical estimate of , specify a list of values for the SIGMA= suboption, and select the value that most nearly linearizes the point pattern. To assess the point pattern, add a diagonal distribution reference line that corresponds to the threshold parameter and the scale parameter with the THETA= and ZETA= suboptions. Alternatively, you can add a line that corresponds to estimated values of and with THETA=EST and ZETA=EST. This line has intercept , and slope exp( ). Agreement between the reference line and the point pattern indicates that the lognormal distribution with parameters , and is a good fit.
Main discussion:	Lognormal Distribution
See also:	the SIGMA= suboption , SLOPE= suboption , THETA= suboption , and ZETA= suboption

LVREF=linetype

specifies the line type for the reference lines that you request with the VREF= option.

Alias:	LV=
Default:	2, which produces a dashed line

MU=value|EST

specifies the mean for a normal Q-Q plot requested with the NORMAL option.

Default:	the sample mean
Requirement:	You must enclose this suboption in parentheses after the NORMAL option.
Tip:	Specify the MU= and SIGMA= suboptions together to request a distribution reference line. Specify MU=EST to request a distribution reference line with equal to the sample mean.

NADJ=value

specifies the adjustment value that is added to the sample size in the calculation of theoretical quantiles. For additional information, see Chambers et al. (1983).

Default:

as recommended by Blom (1958)

NAME='string'

specifies a name for the plot, up to eight characters long, that appears in the PROC GREPLAY master menu.

Default:

UNIVAR

NCOLS=n

specifies the number of columns in the comparative probability plot.

Alias:	NCOL=
Default:	NCOLS=1, if you specify only one class variable, and NCOLS=2, if you specify two class variables.
Requirement:	This option is ignored unless you specify the CLASS statement.
Interaction:	If you specify two class variables, you can use the NCOLS= option with the NROWS= option.

NOFRAME

suppresses the frame around the area that is bounded by the axes.

NORMAL<(normal-suboptions)>

displays a normal Q-Q plot. This is the default if you omit a distribution option.

Tip:	To assess the point pattern, add a diagonal distribution reference line that corresponds to and with the MU= and SIGMA= suboptions. Alternatively, you can add a line that corresponds to estimated values of and with the THETA=EST and SIGMA=EST; the estimates of the mean and the standard deviation are the sample mean and sample standard deviation. Agreement between the reference line and the point pattern indicates that the normal distribution with parameters and is a good fit.
Main discussion:	Normal Distribution
See also:	the MU= suboption and SIGMA= suboption

NROWS=n

specifies the number of rows in the comparative probability plot.

Alias:	NROW=
Default:	2
Requirement:	This option is ignored unless you specify the CLASS statement.
Interaction:	If you specify two class variables, you can use the NCOLS= option with the NROWS= option.

PCTLMINOR

requests minor tick marks for the percentile axis.

PCTLSCALE

requests scale labels for the theoretical quantile axis in percentile units, resulting in a nonlinear axis scale.

Tip:	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 PROBPLOT statement.

RANKADJ=value

specifies the adjustment value that PROC UNIVARIATE adds to the ranks in the calculation of theoretical quantiles. For additional information, see Chambers et al. (1983).

Default:

as recommended by Blom (1958)

SCALE=value

is an alias for the SIGMA= option when you request Q-Q plots with the BETA, EXPONENTIAL, GAMMA, WEIBULL, and WEIBULL2 options and for the ZETA= option when you request the LOGNORMAL option.

See also:

SIGMA= and ZETA=

SHAPE=value(s)|EST

is an alias for the ALPHA=option when you request gamma plots with the GAMMA option, for the SIGMA= option when you request lognormal plots with the LOGNORMAL option, and for the C= option when you request Weibull plots with the WEIBULL, and WEIBULL2 options.

See also:

ALPHA= , SIGMA= , and C=

SIGMA=value(s)|EST

specifies the distribution parameter , where for the quantile plot. The interpretation and use of the SIGMA= option depend on which distribution you specify, as shown in Uses of the SIGMA Suboption .

Uses of the SIGMA Suboption

Distribution Option	Uses of the SIGMA= Option
BETA, EXPONENTIAL GAMMA, WEIBULL	THETA= and SIGMA= request a distribution reference line with intercept and slope .
LOGNORMAL	SIGMA= requests Q-Q plots with shape parameters . The SIGMA= option is required.
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= request a distribution reference line with intercept and slope .

Requirement:	Enclose this suboption in parentheses after the distribution option.
Tip:	To compute a maximum likelihood estimate for , specify SIGMA=EST .

SLOPE=value|EST

specifies the slope for a distribution reference when you request the LOGNORMAL option or WEIBULL2 option.

Requirement:	Enclose this suboption in parentheses after the distribution option.
Tip:	When you use the LOGNORMAL option and SLOPE= to request the line, you must also specify a threshold parameter value with the THETA= suboption. SLOPE= is an alternative to the ZETA= suboption for specifying , because the slope is equal to .
	When you use the WEIBULL2 option and SLOPE= option to request the line, you must also specify a scale parameter value with the SIGMA= suboption. SLOPE= is an alternative to the C= suboption for specifying , because the slope is equal to . For example, the first and second QQPLOT statements produce the same quantile-quantile plots as the third and fourth QQPLOT statements: proc univariate data=measures; qqplot width /lognormal(sigma=2 theta=0 zeta=0); qqplot width /lognormal(sigma=2 theta=0 slope=1); qqplot width /weibull2(sigma=2 theta=0 c=.25); qqplot width /weibull2(sigma=2 theta=0 slope=4);
Main Discussion:	Shape Parameters

SQUARE

displays the Q-Q plot in a square frame.

Default:

rectangular frame

THETA=value|EST

specifies the lower threshold parameter for Q-Q plots when you request BETA, EXPONENTIAL, GAMMA, LOGNORMAL, WEIBULL, or WEIBULL2 option.

Default:	0
Requirement:	You must enclose this suboption in parentheses after the distribution option.
Interaction:	When you use the WEIBULL2 option, the THETA= suboption specifies the known lower threshold , which by default is 0. When you use the THETA= suboption with another distribution option, THETA= specifies for a distribution reference line. To compute a maximum likelihood estimate for , specify THETA=EST. To request the line, you must also specify a scale parameter.

THRESHOLD= value|EST

is an alias for the THETA= option. See the THETA= suboption .

VMINOR=n

specifies the number of minor tick marks between each major tick mark on the vertical axis. QQPLOT does not label minor tick marks.

Alias:	VM=
Default:	0

VREF=value(s)

draws reference lines that are perpendicular to the vertical axis at the value(s) you specify.

See also:

CVREF= option and LVREF= option

VREFLABELS=' label1'... 'labeln'

specifies labels for the reference lines that you request with the VREF= option.

Alias:	VREFLABEL= and VREFLAB=
Restriction:	The number of labels must equal the number of reference lines. Labels can have up to 16 characters.

W=n

specifies the width in pixels for a distribution reference line.

Default:	1
Requirement:	You must enclose this suboption in parentheses after the distribution option.

WEIBULL(C=value(s)|EST <Weibull-suboptions>)

creates a three-parameter Weibull Q-Q plot for each value of the required shape parameter .

Alias:	WEIB
Requirement:	You must specify the shape parameter with the C= suboption.
Interaction:	To create a plot that is based on a maximum likelihood estimate for , specify C=EST. To specify the threshold value , use the THETA= suboption.
Tip:	To obtain a graphical estimate of , specify a list of values in the C= suboption. Then select the value that most nearly linearizes the point pattern. To assess the point pattern, add a diagonal distribution reference line with intercept and slope with the THETA= and SIGMA= suboptions. Alternatively, you can add a line that corresponds to estimated values of and with THETA=EST and SIGMA=EST. Agreement between the reference line and the point pattern indicates that the Weibull distribution with parameters , , and is a good fit.
Main discussion:	Three-Parameter Weibull Distribution
See also	the C= suboption , SIGMA= suboption , and THETA= suboption

WEIBULL2<(Weibull-suboptions)>

creates a two-parameter Weibull Q-Q plot. Use this distribution when your data have a known lower threshold , which by default is 0. To specify the threshold value , use the THETA= suboption.

Note:   The C= shape parameter option is not required with the Weibull2 option.  

Alias:	W2
Default:	0
Interaction:	To specify the threshold value , use the THETA= suboption.
Tip:	An advantage of the two-parameter Weibull plot over the three-parameter Weibull plot is that the parameters 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.
Tip:	To obtain a graphical estimate of , specify a list of values for the THETA= suboption. Then select the value that most nearly linearizes the point pattern. To assess the point pattern, add a diagonal distribution reference line that corresponds to and with the SIGMA= and C= suboptions. Alternatively, you can add a distribution reference line that corresponds to estimated values of and with SIGMA=EST and C=EST. Agreement between the reference line and the point pattern indicates that the Weibull2 distribution with parameters , , and is a good fit.
Main discussion:	Two-Parameter Weibull Distribution
See also:	the C= suboption , SIGMA= suboption , SLOPE= suboption , and THETA= suboption

ZETA= value|EST

specifies a value for the scale parameter for the lognormal Q-Q plots when you request the LOGNORMAL option.

Requirement:	You must enclose this suboption in parentheses after the LOGNORMAL option.
Interaction:	To request a distribution reference line with intercept and slope , specify THETA= and ZETA= .

Theoretical Percentiles of Quantile-Quantile Plots

To estimate percentiles from a Q-Q plot

• Specify the PCTLAXIS option, which adds a percentile axis opposite the theoretical quantile axis. The scale for the percentile axis ranges between 0 and 100 with tick marks at percentile values such as 1, 5, 10, 25, 50, 75, 90, 95, and 99.

• Specify the PCTLSCALE option, which relabels the horizontal axis tick marks with their percentile equivalents but does not alter their spacing. For example, on a normal Q-Q plot, the tick mark labeled is relabeled as because the percentile corresponds to the zero quantile.

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