Summary of Theoretical Distributions

QQPLOT Statement

Summary of Theoretical Distributions

You can use the QQPLOT statement to request Q-Q plots based on the theoretical distributions summarized in the following table:

Table 10.14: QQPLOT Statement Distribution Options

			Parameters
Distribution	Density Function p(x)	Range	Location	Scale	Shape

Beta	$\frac{(x-\theta )^{\alpha-1}(\theta+\sigma-x)^{\beta-1}} {B(\alpha,\beta)\sigma^{(\alpha+\beta-1)}}$	$\theta\lt x \lt\theta+\sigma$	$\theta$	$\sigma$	$\alpha$ , $\beta$
Exponential	$\frac{1}{\sigma}\exp(-\frac{x-\theta}{\sigma})$	$x \geq \theta$	$\theta$	$\sigma$
Gamma	$\frac{1}{\sigma\Gamma(\alpha)} (\frac{x-\theta}{\sigma})^{\alpha-1} \exp(-\frac{x-\theta}{\sigma})$	$x\gt\theta$	$\theta$	$\sigma$	$\alpha$
Lognormal	$\frac{1}{\sigma\sqrt{2\pi}(x-\theta)} \exp(-\frac{(\log(x-\theta)-\zeta)^2}{2\sigma^2})$	$x\gt\theta$	$\theta$	$\zeta$	$\sigma$
(3-parameter)
Normal	$\frac{1}{\sigma\sqrt{2\pi}} \exp(-\frac{(x-\mu)^2}{2\sigma^2})$	all x	$\mu$	$\sigma$
Weibull	$\frac{c}{\sigma}(\frac{x-\theta}{\sigma})^{c-1} \exp(-(\frac{x-\theta}{\sigma})^c)$	$x\gt\theta$	$\theta$	$\sigma$	c
(3-parameter)
Weibull	$\frac{c}{\sigma}(\frac{x-\theta_0}{\sigma})^{c-1} \exp(-(\frac{x-\theta_0}{\sigma})^c)$	$x\gt\theta_0$	$\theta_0$	$\sigma$	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.

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