Plotting Positions
The choice of quantiles from a theoretical distribution has occasioned much discussion. A natural choice, given a sample of size n, is k / n for k = 1, ..., n, as these are the quantiles that the sampling distribution realizes. Unfortunately, the last of these, n / n, corresponds to the 100th percentile – the maximum value of the theoretical distribution, which is often infinite. To fix this, one may shift these over, using (k − 0.5) / n, or instead space the points evenly in the uniform distribution, using k / (n + 1). This last one was suggested early on by Weibull, and recently it has been argued to be the definitive position by Lasse Makkonen. The claimed unique status of this estimator was rebutted by N.J. Cook. Many other choices have been suggested, both formal and heuristic.
Read more about this topic: Q-Q Plot
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