Poisson
The Poisson distribution scaled by a total count. Use it for histograms of counts, such as the number of radioactive decays recorded in many equal time windows.
Parameters
- Total number of intervals: the sum of y over all x = 0, 1, 2, …
- Mean number of counts per interval, which is also the variance.
Tips
- x is the count in one interval (0, 1, 2, …) and y is how many intervals gave that count. x! is evaluated with the gamma function, so non-integer x is accepted, but the model is meant for whole numbers.
- This is a least-squares fit of the Poisson shape, not a maximum-likelihood fit of the counts; with few counts per bin the two can differ.
- √y is a common choice of δy for counts, but every active uncertainty must be positive, so a bin with no counts needs another value.