The Rayleigh distribution has the probability density function:

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

q <= x < ∞, b > 0

where

b |
is the Scale parameter |

q |
is the Threshold (location) parameter |

e |
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.