Mixture of Distributions

[pappi]

I have a dataset. The data items indicate 'time of arrivals'. The distribution is actually unknown.

So you might be thinking it is 'Poisson' distribution, if you did, why did you think so?
If we assume that it is Poisson, how do we test for the hypothesis that it IS STATISTICALLY POISSON?

I also want to determine how many Poisson processes generated the data.
i.e, to test whether it is a mixture of Poissons, and if yes then how many Poisson processes.

I don't know if my questions can be statistically answered.

Basically, I have data. I need to determine the distribution - i am not sure if it is Poisson at all, whether it is a mixture of distributions and if so how many mixtures and what are their statistics.


Thanks!
pappi

[economicus]

Well, the poisson distribution is often the first model considered for random counts. To test for it...you should know that the poisson distribution has a property that the mean of distribution is equal to the variance. So if you find out that the variance is substantially larger than the mean, it's not a good approximation. Usually, the negative binomial distribution is considered instead of poisson if the latter fails.

You can get more insights into this theme, for instance, in Rice: Mathematical Statistics and Data analysis.