4.1.1 Probability distribution
In EDXRF counting, the probability of obtaining a measurement result x when the "true" value is N0 can be well described following the Poisson distribution:
and the standard deviation of the true value is
The Poisson attribution to the counting statistics can be applied to both the number of counts in each channel of an EDXRS spectrum as well as to the sum over a number of channels. As it will be demonstrated in the following section, in order to accept a given measurement as different from noise, it has to be at least three times larger than the square root of the noise.
The fact that the uncertainty of the measurement can be calculated from the measurement result is of great relevance. A given target relative uncertainty can be pursued by obtaining a suitable measurement result:
When the interval of x is very small and the number of counts N0 is very large, the Poisson distribution transforms into a Gaussian distribution:
and the standard deviation of the true value is
