Lognormal Distribution for Quantile-Quantile Plots

The lognormal distribution has the probability density function:

f(x) = 1/[(x-q)s(2p)1/2 ] * e^[-{log(x-q)-m]}2 /2s2]

q < x < ∞, μ > 0, s > 0

where

m

is the Scale parameter

s

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...)

The standardized Lognormal distribution with Shape parameter will be used to find the best fitting distribution function. The Shape parameter can be specified in one of two ways:

  1. On the Quantile-Quantile Plots - Advanced tab, enter user-defined values for Shape1 and Shape2 and clear the Compute parameters from: check box.

  2. Estimate the Shape parameter by selecting the Compute parameters from: check box and entering a user-defined Threshold parameter. The Shape parameter is estimated using either the maximum likelihood or matching moments approximation (see below).

In general, if the points in the Q-Q plot form a straight line, then the respective family of distributions (Lognormal distribution with the Shape parameter s in this case) 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 (m) parameters, respectively.