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A New Proposal to Adjust a Straight Line to a normal q-q plot

Journal of Mathematics and System Science 2012年第5期2卷 327-333页

作者： Sonia Castillo-Gutierrez Emilio Damian Lozano-Aguilera Maria Dolores Estudillo-Martinez Department of Statistics and Operations Research University of Jadn Jadn 23071 Spain

In this paper a new proposal of a straight line, the ＂modified Tukey＇s line＂, for fitting to a normal quantile-quantile plot, or normal q-q plot, is presented. This probability plot allows us to determine whether a set of sample observations is distributed according to a normal distribution. For this, the sample quantiles are represented against the quantiles of a theoretical probability model, which in this case is the normal distribution. If the data set follows the above mentioned distribution, the plotted points will have a rectilinear configuration. To verify this, there are different alternatives for fitting a straight line to the plotted points. Among the straight lines which can be fitted to a q-q plot, in this paper, besides the proposed straight line, the following straight lines are considered： straight line that passes through the first and third quartiles, straight line that passes through the 10th and 90th percentiles, straight line fitted by the method of least squares, straight line with slope s and constant the average of the data set, Theil＇s line and Tukey＇s line. In addition, an example, in which there are represented the different straight lines considered and the proposed straight line on a normal q-q plot obtained for the same set of observations, is developed. In this example the existing differences among the straight lines are observed.

关键词： normal q-q plot straight line modified Tukey's line.

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Influence of the Fitted Straight Line for Confidence Bands Algorithm in q-q plots

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Open Journal of Statistics 2021年第6期11卷 925-930页

作者： Sonia Castillo-Gutiérrez María Dolores Estudillo-Martínez Emilio Damián Lozano-Aguilera Department of Statistics and Operations Research University of Jaén Jaén Spain

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.

关键词： normal q-q plot Confidence Bands Fitted Straight Line Goodness of Fit

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