Rayleigh Distribution for Quantile-Quantile 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...)

The inverse distribution function (of probability a) is (for q=0): {-2b2[log(1-a)]}1/2

The standardized Rayleigh distribution function is used to determine the best fitting distribution.

In general, if the points in the Q-Q plot form a straight line, then the respective family of distributions (Rayleigh distribution) provides a good fit to the data; in that case, the intercept and slope of the fitted line can be interpreted as graphical estimates of threshold (q) and scale (b) parameters, respectively.