Ok then I suggest you use 10 min time intervals to avoid getting lots of zeros. If you have 6 timeslots per hour then you can measure for 10 hours to get 60 samples. Of course the more samples you can get the better

If you found the constant then you could subtract it from every measurement and make a confidence interval for the mean. Since you can change your time intervals to 1 minute it should be very easy to find the constant if you are only monitoring 10 houses.That was bad news I think!If I find the constant, then I could subtract it and then do the Pearson X^2 ?, finding more high values weighting the tail than for the polulation? I feel it would be the opposite. or is it due to noise that squared get higher weight since that is usually not Zero centered ?

On a Poisson, What is over-dispersion really comming from