Exponential Distribution for Quantile-Quantile Plots

The exponential distribution has the probability density function:

f(x) = le[-l(x-q)]

0 <= x < ∞, l > 0, q<x

where

q is the Threshold (location) parameter
l is the Scale parameter (an alternative parameterization is Scale parameter l=1/b)
e is the base of the natural logarithm, sometimes called Euler's e (2.71...)
  • The inverse distribution function (of probability a) is: -1/l*log(1-a)
  • The standardized exponential distribution function is used to determine the best

In general if the points in the Q-Q plot form a straight line, then the respective family of distributions (Exponential 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 the threshold (q) and scale (l) parameters, respectively.