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 ... x_nThese observed values are plotted against one axis of the graph; on the other axis the plot will show: F^-1((i-r_adj) / (n+n_adj)) where i is the rank of the respective observation, r_adj and n_adj 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 r_adj and n_adj 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.