A distribution free plotting position |
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| Authors: | G-H Yu C-C Huang |
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| Institution: | (1) Water Resources Management and Policy Research Center, Tamkang University, Tamsui 251, Taiwan, TW;(2) Department of Information Management, Yuan-Ze University, Jung Li 320, Taiwan, TW |
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| Abstract: | Many plotting position formulae have been proposed for the past few decades. These formulae are derived or obtained under
some specific assumption of probability distribution. Because in practice the data are often plotted in order to determine
its probability distribution, it causes difficulty and confusion in selecting the plotting position formula. The objective
of this study is to find a plotting position formula which is distribution free. In this study, the plotting position formulae
corresponding to the order statistic mean, mode and median are investigated. The order statistic mean, mode and median values
are determined by numerical integration and differentiation, and the corresponding plotting position formulae are obtained
by regression analysis. The results indicate that both the plotting position formulae for the order statistic mean and mode
vary with the distribution of data, but the plotting position formula for the order statistic median is distribution free.
The distribution free plotting position formula for the order statistic median is proposed in this study as (i−0.326)/(n+0.348). |
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