QQPLOT Statement: CAPABILITY Procedure

Summary of Theoretical Distributions

You can use the QQPLOT statement to request Q-Q plots based on the theoretical distributions summarized in Table 5.71.

Table 5.71: QQPLOT Statement Distribution Options

				Parameters
Distribution	Density Function $p(x)$		Range	Location	Scale	Shape
Beta	$\frac{(x-\theta )^{\alpha -1}(\theta +\sigma -x)^{\beta -1}}{B(\alpha ,\beta )\sigma ^{(\alpha +\beta -1)}}$		$\theta < x <\theta +\sigma$	$\theta$	$\sigma$	$\alpha$ , $\beta$
Exponential	$\frac{1}{\sigma }\exp \left(-\frac{x-\theta }{\sigma }\right)$		$x \geq \theta$	$\theta$	$\sigma$
Gamma	$\frac{1}{\sigma \Gamma (\alpha )} \left(\frac{x-\theta }{\sigma }\right)^{\alpha -1} \exp \left(-\frac{x-\theta }{\sigma }\right)$		$x>\theta$	$\theta$	$\sigma$	$\alpha$
Gumbel	$\frac{e^{-(x-\mu )/\sigma }}{\sigma } \exp \left( -e^{-(x-\mu )/\sigma }\right)$		all x	$\mu$	$\sigma$
Lognormal	$\frac{1}{\sigma \sqrt {2\pi }(x-\theta )} \exp \left(-\frac{(\log (x-\theta )-\zeta )^{2}}{2\sigma ^{2}}\right)$		$x>\theta$	$\theta$	$\zeta$	$\sigma$
(3-parameter)
Normal	$\frac{1}{\sigma \sqrt {2\pi }} \exp \left(-\frac{(x-\mu )^2}{2\sigma ^{2}}\right)$		all x	$\mu$	$\sigma$
Generalized	$\alpha \neq 0$	$\frac{1}{\sigma }{(1 - \alpha (x-\theta )/\sigma )}^{1/\alpha -1}$	$x > \theta$	$\theta$	$\sigma$	$\alpha$
Pareto	$\alpha = 0$	$\frac{1}{\sigma }\exp (-(x-\theta )/\sigma )$
Power Function	$\frac{\alpha }{\sigma }\left(\frac{x-\theta }{\sigma }\right)^{\alpha -1}$		$x > \theta$	$\theta$	$\sigma$	$\alpha$
Rayleigh	$\frac{x-\theta }{\sigma ^2}\exp (-(x-\theta )^2/(2\sigma ^2))$		$x \geq \theta$	$\theta$	$\sigma$
Weibull	$\frac{c}{\sigma }\left(\frac{x-\theta }{\sigma }\right)^{c-1} \exp \left(-\left(\frac{x-\theta }{\sigma }\right)^{c}\right)$		$x>\theta$	$\theta$	$\sigma$	c
(3-parameter)
Weibull	$\frac{c}{\sigma }\left(\frac{x-\theta _0}{\sigma }\right)^{c-1} \exp \left(-\left(\frac{x-\theta _0}{\sigma }\right)^{c}\right)$		$x>\theta _0$	$\theta _0$	$\sigma$	c
(2-parameter)			(known)

You can request these distributions with the BETA, EXPONENTIAL, GAMMA, LOGNORMAL, NORMAL, WEIBULL, and WEIBULL2 options, respectively. If you do not specify a distribution option, a normal Q-Q plot is created.