Hermitian quantile curves as statistical plots

Abstract

Graphical tools such as Q-Q plots are integral parts of exploratory data analyses, and of the post-hoc analyses such as the residual analysis in regression modeling. In this note we offer some practical continuous and smooth continuous alternatives to various empirical plots. Specifically, the Hermitian quantile function estimator defined by Mudholkar et al. (1996) is employed for developing alternatives to the well known Q-Q plots, quantile-box plots, P-P plots, normal probability plots, and the plots involving the shift function and various symmetry functions.

Keywords:

• exploratory data analysis
• L-estimators
• order statistics
• Q-Q plot