Influence of the Fitted Straight Line for Confidence Bands Algorithm in Q-Q Plots

Sonia Castillo-Gutiérrez,Emilio Damián Lozano-Aguilera,María Dolores Estudillo-Martínez

doi:10.4236/ojs.2021.116054

Abstract

Confidence bands in a Normal Q-Q Plot allow us to detect non-normality of a data set rigorously, and in such a way that the conclusion does not depend on the subjectivity of the observer of the graph. In the construction of the graph, it is usual to fit a straight line to the plotted points, which serves both to check the hypothesis of normality (linear configuration of the plotted points) and to produce estimates of the parameters of the distribution. We can opt for dif-ferent types of lines. In this paper, we study the influence of five types of fitted straight lines in a Normal Q-Q Plot used for construction the confidence bands based on the exact distribution of the order statistics.

Highlights

Normal probability plots and, in particular, Normal Q-Q Plots, are used to determine if a set of observations derives from a normal distribution
We study the influence of five types of fitted straight lines in a Normal Q-Q Plot used for construction the confidence bands based on the exact distribution of the order statistics
Confidence bands represented in Q-Q Plot depend on the fitted straight line, so if we change the straight line, the confidence bands change, and the conclusion may be different

Summary

Introduction

In particular, Normal Q-Q Plots, are used to determine if a set of observations derives from a normal distribution. That is why this technique is often called “informal technique” To avoid this problem, the confidence bands or acceptance region [5] are used to determine whether or not a data set has a normal distribution, so that the conclusion is the same regardless of the observer of the graph. Some of the confidence bands depend on the straight line represented on the Normal Q-Q Plot to be able to be constructed. The plotting positions, the fitted straight line and the confidence bands are key elements in a Normal Q-Q Plot. We will focus on the analysis of five types of straight lines and on the confidence bands based on the exact distribution of the order statistics [5]. In the last section, the conclusions of this study are presented

Fitted Straight Lines in a Q-Q Plot

Confidence Bands Based on the Exact Distribution of the Order Statistics

Example 1

Example 2

Conclusions