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Computation of optimal plotting points based on Pitman closeness with an application to goodness-of-fit for location-scale families. (English) Zbl 1255.62144
Summary: Plotting points of order statistics are often used in the determination of goodness-of-fit of observed data to theoretical percentiles. Plotting points are usually determined by using nonparametric methods which produce, for example, the mean- and median-ranks. Here, we use a distribution-based approach which selects plotting points (quantiles) based on the simultaneous-closeness of order statistics to population quantiles. We show that the plotting points so determined are robust over a multitude of symmetric distributions and then demonstrate their usefulness by examining the power properties of a correlation goodness-of-fit test for normality.

MSC:
62G30 Order statistics; empirical distribution functions
62-09 Graphical methods in statistics (MSC2010)
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