I am trying to use poissonian distribution to validate photon emission of x-ray source. Photons counts are recorded at 100ms intervals using a photon counting detector. If the photon distribution is Poissonian then we can deduce that source is ok, otherwise we can predict that source has a problem.
I used Minitab to compare observed and expected number of counts, which gives a correct result. But my aim is to program the validation process. But when I tried to calculate Poisson probabilities manually, it seems all wrong. Counts are bin center values. The mean of the distribution is 2105,
count 1972 1999 2026 2053 2081 2108 2135 2162 2189 2216
Freq 3 10 30 66 100 105 93 65 23 5
These are the corresponding probabilities which is calculated using Excel Poisson function (POISSON.DIST)
0.000131 0.000621 0.00205 0.004721 0.007624 0.008656 0.006879 0.003885 0.001567 0.000453
Those probability values make no sense at all. Can someone explain what I have done wrong and how to calculate correct probabilities and expected frequencies?
Thanks
The Excel values are the probability of getting exactly your bin center value. They sum to about $0.036$ and your bins are $27$ wide. $27 \cdot 0.036 \approx 1$. You should get the value for each number of counts from $2095$ through $2121$ and add them up to get the probability of your $2108$ bin. It will not be far from $27 \cdot 0.008656$. Now compare these probabilities to the fraction of events in each bin.