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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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