Objective Judgement on Q-Q Plot for Testing Laplace Distribution

Abstract

Q-Q plot is one of the graphical tools for evaluating the validity of an underlying distribution which compares quantiles of a sample against the quantiles of the distribution. In this paper, we focus on how a Q-Q plot can be augmented by intervals for all the points so that, if the population distribution is Laplace then all the points should fall into the corresponding intervals simultaneously with probability $1-\alpha$. Therefore, the major concern of this paper is to construct the objective mean based graphical tests to assess whether the plotted points fall close to the straight line. Simulations are used to compare powers among graphical tests and some popular non-graphical Anderson-Darling and Cramer-von-Mises tests. Based on this power study, the tests which have higher powers are recommended to apply real world problems and should be used in what circumstances. Finally, the example is provided to illustrate the methods.