Plotting positions for Pearson type-III distribution

A great deal of data is generated by the Monte Carlo method to develop a plotting position formula for Pearson type-III distribution for the C s coefficients of skewness of parent distribution in the range of between 0 and 2. This formula can be applied to both symmetrical and unsymmetrical parent distributions and will also provide unbiased and efficient estimations of quantiles. This formula compares favorably with all currently available formulas. In order to use this developed plotting position formula, a coefficient b must be determined. These b-values are mainly dependent on the values of C s and the order number of the arranged sample.