Weibull Distribution for Probability-Probability Plots

The Weibull distribution has the probability density function:

f(x) = c/b*[(x-q)/b]c-1 * e^ -[(x-q)/b]c

0 <= x < ∞, b > 0, c > 0, q > 0

where

b is the Scale parameter
c is the Shape parameter
q is the Threshold (location) parameter
e is the base of the natural logarithm, sometimes called Euler's e (2.71...)

Compute from data

When you clear this check box (on the Probability-Probability Plots

Advanced

tab), you then need to specify the Shape and Scale parameters (b and c, respectively) as well as the Threshold parameter q. When you select this check box and specify the Threshold parameter q, Statistica estimates both the Shape and Scale parameters (b and c, respectively) from the data.

In general, if the observed points follow the Weibull distribution with the respective parameters, then they will fall onto the straight line in the P-P plot.

Note: you can use the Quantile-Quantile plot to obtain the parameter estimates (for the best fitting distribution from a family of distributions) to enter here.

Use Max. Likelihood

The Use Max. Likelihood check box is displayed when you select the Weibull distribution on the Probability-Probability Plots -

Advanced

tab.

  • When you select this check box, Statistica uses the maximum likelihood method to estimate the Shape and Scale parameters of the Weibull distribution (see Evans, Hastings, & Peacock, 1993, for details).
  • When you clear the check box, then the method of matching moments is used.