The best way to make and update a Multinomial distribution?

Question

I want to fit a distribution to a set of data I have. My questions are:

1. How can I know the best distribution that can be fitted. The expectation is that the final distribution be a Binomial or a Multinomial distribution. (is it good to use kernel density estimation?)

2. What is the best way to update the created distribution when a new data arrives?

Thank you!

Answer 1

Let me try to answer your questions.

1. How can I know the best distribution that can be fitted. The expectation is that the final distribution be a Binomial or a Multinomial distribution. (is it good to use kernel density estimation?)

First it is a very hard question to assess which distribution best fits data if we do not know anything about it, especially since there are so many different shapes of distributions out there. Now if we focus on the binomial and multinomial distributions, we could try fitting this to the data. So we estimate the parameters of these distributions according to the data. This could for instance be done by maximum likelihood estimation. A way to test whether this fit is a good one is to make a qq-plot to visualize if the quantiles match. Another thing to look at is hypothesis testing. Think of the Kolmogorov-Smirnov test as a way to test whether the fitted distribution matches the emprical data. We can choose a confidence level and accept or reject the proposed distribution based on this.

2. What is the best way to update the created distribution when a new data arrives?

If you are doing this you are basically using Bayesian statistics. Using this if we describe a prior distribution we can update our distribution using the new data. If you are unfamiliar with this I recommend searching on Wikipedia.