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
Famous quotes containing the words plotting and/or positions:
“I’m plotting revolution against this lie that the majority has a monopoly of the truth. What are these truths that always bring the majority rallying round? Truths so elderly they are practically senile. And when a truth is as old as that, gentlemen, you can hardly tell it from a lie.”
—Henrik Ibsen (1828–1906)
“The season developed and matured. Another year’s installment of flowers, leaves, nightingales, thrushes, finches, and such ephemeral creatures, took up their positions where only a year ago others had stood in their place when these were nothing more than germs and inorganic particles. Rays from the sunrise drew forth the buds and stretched them into long stalks, lifted up sap in noiseless streams, opened petals, and sucked out scents in invisible jets and breathings.”
—Thomas Hardy (1840–1928)