The UNIVARIATE Procedure

Estimating Shape Parameters Using Q-Q Plots

Some of the distribution options in the PROBPLOT or QQPLOT statements require you to specify one or two shape parameters in parentheses after the distribution keyword. These are summarized in Table 4.34.

You can visually estimate the value of a shape parameter by specifying a list of values for the shape parameter option. A separate plot is produced for each value, and you can then select the value of the shape parameter that produces the most nearly linear point pattern. Alternatively, you can request that the plot be created using an estimated shape parameter. See the entries for the distribution options in the section Dictionary of Options (for the PROBPLOT statement) and in the section Dictionary of Options (for the QQPLOT statement).

Note: For Q-Q plots created with the WEIBULL2 option, you can estimate the shape parameter $c$ from a linear pattern by using the fact that the slope of the pattern is $\frac{1}{c}$ .

Table 4.34: Shape Parameter Options

Distribution Keyword	Mandatory Shape Parameter Option	Range
BETA	ALPHA= $\alpha$ , BETA= $\beta$	$\alpha >0$ , $\beta >0$
EXPONENTIAL	None
GAMMA	ALPHA= $\alpha$	$\alpha >0$
GUMBEL	None
LOGNORMAL	SIGMA= $\sigma$	$\sigma >0$
NORMAL	None
PARETO	ALPHA= $\alpha$	$\alpha >0$
POWER	ALPHA= $\alpha$	$\alpha >0$
RAYLEIGH	None
WEIBULL	C= $c$	$c>0$
WEIBULL2	None