Mathematical properties of the QQ plot

Quantile-Quantile (QQ) plots are a common tool to visualise a comparison between a univariate data vector and a distribution function that is posited as the source of this data.  This project examines the mathematical properties of the QQ plot by examining the mathematical properties of order statistics.  We seek to explain how the patterns in the data relate to moment properties and other aspects of the underlying distribution of the data (relative to the posited distribution).  We seek to explain phenomena such as data clumping and tail variation via mathematical analysis.