New Plotting‐position Formula For Pearson Type‐III Distribution

Abstract

The main objective of this paper is to develop a new unbiased plotting‐position formula for the Pearson type‐III (P3) distribution. The probabilityweighted moment (PWM) method is used to estimate the exact plotting positions. It is shown that the estimation of plotting positions for the P3 distribution using the PWM technique has several advantages over both the direct numerical integration method and the Monte Carlo simulation procedure. For the convenience of practical application, a simple formula representing a very good approximation of the exact plotting positions is proposed. It is found that the suggested formula gives a better agreement with the exact plotting positions than several existing formulas. Further, the proposed formula is more flexible, because it can take explicitly into account the skewness coefficient of the underlying distribution. It can be concluded that the plotting formula developed in this study is the most appropriate for the P3 distribution and for both small and large samples. Finally, the development of probability papers for the P3 distribution for various skewness values is presented. Results of a numerical example have demonstrated the advantages related to the use of these special probability papers in engineering practice.