Q-Q Plot Dialog
This dialog is activated by selecting the Q-Q Plot... command from the Plot -> Statistical Graphs menu. It can be used in order to create and customize a Q-Q (quantile-quantile) plot of the selected data column in the active table window.
The N valid input data values xi are first sorted ascendingly: x1 ≤ x2 ≤ ... ≤ xN. After that the index i of the ordered values is used to calculate a score (s) using one of the five methods listed below:
- Blom
(default): s = (i - 0.375)/(N + 0.25)
- Benard
s = (i - 0.3)/(N + 0.4)
- Hazen
s = (i - 0.5)/N
- VanDerWaerden
s = i/(N + 1)
- KaplanMeier
s = i/N
The sorted values are represented on the Q-Q plot by points whose X coordinates are the xi values and whose Y coordinates are calculated using the inverse of the cumulative distribution functions of the s scores calculated above.
There are five distributions available for Q-Q plots and the inverse of their cumulative distribution functions are calculated using the following formulas (available with muParser as script engine):
- Normal
(default): normalinv(s, m, sd), where m is the arithmetic mean and sd is the standard deviation of the input data set.
- Lognormal
logninv(s, scale, shape)
- Exponential
expinv(s, m), where m is the arithmetic mean of the input data set.
- Weibull
wblinv(s, scale, shape)
- Gamma
gaminv(s, shape, scale)
The scale and shape parameters that are used for the Lognormal, Weibull and Gamma distributions are calculated using the maximum likelihood estimation (MLE) method.