Four-Point Method

The Four Point method of curve fitting is used to provide faster approximations than generally possible using an All Points method . The type of distribution (Bounded, Unbounded, or Log Normal) is chosen based on the value of the discriminant (d), calculated as follows:

where 

x0, x1, x2, x3 are the kth data values (when the data is rank ordered), corresponding to selected percentiles (Fo) of the Normal distribution, and n is the total number of data points in the analysis. If there are more than 30 data values, the percentiles used for calculating the fit are at z-values of +.524, -.524, +1.572 and -1.572, where z is the standardized normal variate. (These correspond to percentiles of approximately 6%, 20%, 70%, and 94%). If there are 30 or less data values, the percentiles used for calculating the fit are at z-values of +.427, -.427, +1.281 and -1.281. (These correspond to percentiles of approximately 6%, 10%, 90%, and 94%).

If the calculated discriminant d is greater than 1.001, then an Unbounded distribution is chosen. If the value is less than 0.999, then a Bounded distribution is chosen. A discriminant equal to or between the two values results in a Log Normal fit. (Slifker and Shapiro).

The fit parameters for the transformation are calculated by solving the transformation equation shown above (for the chosen distribution type) at the four selected percentiles. These four equations are then solved for the fit parameters.

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