PCM-2 Manual.pdf - Voss Associates

Gaussian Distribution Function
An approximation can be applied to the Poisson Distribution Function when values of a function's
mean (.\ in the Poisson Distribution Function) become larger than about 20. This approximation,
known as the Gaussian or Normal Distribution Function is extensively used in radiological counting
statistics. It is familiar to many as the "Bell Curve" defined by Eq. 30 operating on "x".
lex)
x'
e 2
Eq. 30
Figure 3, Gaussian Distribution Function
The domain of this function is all real numbers. The function is centered about 0, whereas a
sample's distribution is centered about its mean. Thus, the first step in applying the Gaussian
Distribution Function to a sample is to subtract the sample's mean from each data point so as to
center the data about zero. Secondly, the distribution of a sample is scaled to the independent
variable "x" by its standard deviation. The Cumulative Gaussian Distribution Function is normalized,
i.e., the sum of all probabilities is 1, geometrically interpreted as the total area under the normal
curve. The probability that "x or less" will be encountered within a sample is defined as the
cumulative distribution from - 00 to x as shown by Eq. 31.
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