PCM-2 Manual.pdf - Voss Associates

P(x)
Eq.31
As illustrated by Figure 4, Eq. 31 is the area under the Gaussian Distribution Curve from -00 to x.
Figure 4, Cumulative Gaussian Distribution Function
Much data related to statistical distribution functions is readily available in tabular form in math
handbooks. Table 2 presents values for the Cumulative Normal Distribution operating on values of
"x" from 0.00 through 5.00. The sidebar that follows Table 2 illustrates Hastings' Best
Approximation for calculating P(x), and a method for calculating the Inverse Cumulative Normal
Distribution. The inverse function is used to return "x" when the desired P(x) is known. Hastings'
Best Approximation operates on positive values of x and results in an error of less than or equal to
7.5 x 10- 8 • The Inverse Approximation operates on the domain of 0.5"::;' P(x) < 1 with an
associated error that is less than or equal to 4.5 x 10-4. These algorithms are ideal for inputting into a
programmable calculator, making the data available when a table is not handy.
PCM2.MAN