Rayleigh Distribution for Probability-Probability Plots

The Rayleigh distribution has the probability density function:

f(x) = (x-q)/b2 * e ^ -[(x-q)2 /2b2]

q <= x < ∞, b > 0



is the Scale parameter


is the Threshold (location) parameter


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 Scale parameter b as well as the Threshold parameter q. When you select this check box and specify the Threshold parameter q, STATISTICA estimates the Scale parameter b from the data.

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