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It is my first question here and I am not a statistian. So - I am sorry for any mistake - please correct me.

I have data from measuring a feature of a number of entities (continious data). As I don't know which distribution to expect, the feature range has been divided into fixed bins. For each independet experiment, I retrieve the entity counts for each bin. That means for each bin, I have as many counts as experiments.

Example:

Experiment 1 - Bin 1 - 20
Experiment 2 - Bin 1 - 19
Experiment 3 - Bin 1 - 22

Experiment 1 - Bin 2 - 5
Experiment 2 - Bin 2 - 9
Experiment 3 - Bin 2 - 7

Looking at the counts of a single bin: Which distribution would I expect?

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Within an experiment, an observation can only end up in one bin.

If the observations are independent before you bin them, you would look at a multinomial distribution for each experiment.

That is considering experiment $i$, then if the count in bin $j$ is $X_{i,j}$, then $(X_{i,1},X_{i,2},X_{i,3},...,X_{i,n})$ would be multinomial with parameters $n_i$ (the total number of values in experiment $i$) and the set of population proportions for that experiment.

If you focus on a single bin (compared to all others), that would be binomial.

If you consider the set of counts in the bins for all experiments, then if the counts are independent across experiments you'd have an independent collection of multinomials.

If you consider the set of counts in one bin over all experiments, that would be a collection of independent binomial observations.

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  • $\begingroup$ I think - I am interested in the last point you mentioned. I am just not sure whether I can use that information for my final problem :-) I might need to reformulate my problem... $\endgroup$
    – Antje Janosch
    Commented Jul 1, 2015 at 9:07
  • $\begingroup$ added a sentence I neglected to add before. $\endgroup$
    – Glen_b
    Commented Jul 1, 2015 at 10:38
  • $\begingroup$ Question: Instead of a multinomial (first case you mentioned) - could it be a hypergeometric distribution (as it is without replacement...)? $\endgroup$
    – Antje Janosch
    Commented Jul 7, 2015 at 6:42
  • $\begingroup$ Possibly hypergeometric, though nothing in the question suggested it to me. Could you describe the situation more explicitly (in your question)? $\endgroup$
    – Glen_b
    Commented Jul 7, 2015 at 8:00
  • $\begingroup$ Let's compare one experiment to this: Within a fish tank 100 fish grew up. I take a big net, get as much fish as possible and measure their length. Then I put each fish into one of five bins according to their length. (10-15cm, 15-20cm, ...) From my prior knowledge, I have a certain expectation how the fishes should be distributed (20% in the first bin, 40% in the second bin, ...). And I would like to test, if the acutal count fit to that. Does it make it a bit more clear? (I will put it into muy questions if it helps at all) $\endgroup$
    – Antje Janosch
    Commented Jul 7, 2015 at 9:19

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