# How to detect a number of binomial distributions from a set of data?

Say I have n sets of data where each set of data has a binomial distribution. The n sets of data are then combined into one set. If I take the combined set of data, how would I go about detecting that this set is made up from n individual sets ?

I have only a limited background in statistics, so here is an example to clarify the question: I collect the amount of energy used by an appliance at 3pm each day for a number of months Generally the amount of energy used follows these rules: - On Monday to Friday, the appliance uses 3000 kWh (mean value) - On Saturday, the appliance uses 200 kWh (mean value) - On Sunday, the appliance uses 50 kWh (mean value)

I want to be able to take all the 3pm readings every day for a year and then be able to detect that the readings can be broken into the 3 sets as described above. After I deduce that there are 3 sets of data, I plan to calculate the mean value with std dev etc. for each individual set.

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If you take the data every day, don't you know the day of the week? And why would you suppose there is a binomial distribution? –  Henry Jun 20 '11 at 21:27
If you have an idea as to the distribution of the energy used in each subgroup, then you may want to look up a mixture model: mixture models –  Max Jun 20 '11 at 21:49
@Henry yes, but what I really want to try to achieve is to get a set of data made of of tuples with (energy value, date) and figure out of there is such a relationship like the one where the expected energy is usually around 50kWh on some days and around 3000 kWh on other days. Then I want to algorithm to tell me which days I will expect a higher value and which days I will expect a lower value. –  Philip Clarke Jun 22 '11 at 8:29
@Max, thanks I think mixture models are exactly what I need to look at here. –  Philip Clarke Jun 22 '11 at 8:31
@Henry it should have been "normal" distribution, thanks for spotting that –  Philip Clarke Jun 23 '11 at 15:13
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## 1 Answer

If you have an idea as to the distribution of the energy used in each subgroup, then you may want to look at mixture models.

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