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# q-q plot

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A plot for comparing two probability distributions, usually the sample distribution function and a theoretical distribution function. The sample values are ranked in order: x(1)x(2)≤…≤ x(n). Define the sample cumulative proportion as pj, typically calculated as (j−½)/n, and denote the theoretical distribution function by F. In a q-q plot, F−1(pj) is plotted against x(j), for all j. If the sample has come from the theoretical distribution, the plotted values will lie on an approximate straight line. Specialized graph paper, that has the values of F−1 marked for interesting values of p is called probability paper.

The p-p plot is entirely equivalent: F(x(j)) is plotted against pj. Once again, if the sample has come from the theoretical distribution, the plotted values will lie on an approximate straight line. A plot of this type is called a probability plot. See also normal probability paper.

Subjects: Probability and Statistics.

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