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