Quantile-Quantile Plots

You can visually check for the fit of a theoretical distribution to the observed data by examining the quantile-quantile (or Q-Q) plot (also called Quantile Plot).

In this plot, the observed values of a variable are plotted against the theoretical quantiles. A good fit of the theoretical distribution to the observed values would be indicated by this plot if the plotted values fall onto a straight line. To produce a Q-Q plot, the program will first sort the n observed data points into ascending order, so that:

x1 x2 ... xn
These observed values are plotted against one axis of the graph; on the other axis the plot will show:
F-1((i-radj) / (n+nadj)) where i is the rank of the respective observation, radj and nadj are adjustment factors ( 0.5) and F-1 denotes the inverse of the probability integral for the respective standardized distribution. The resulting plot (see below) is a scatterplot of the observed values against the (standardized) expected values, given the respective distribution. Note also that the adjustment factors radj and nadj ensure that the p-value for the inverse probability integral will fall between 0 and 1, but not including 0 and 1 (see Chambers, Cleveland, Kleiner, and Tukey, 1983.