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 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 StartFraction 1 Over c EndFraction.

Table 34: Shape Parameter Options

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


Last updated: April 16, 2025