# How to estimate return period amount at different distributions

1. Jul 17, 2012

### re444

I have yearly rain amounts and want to estimate the rain with 100 year return period assuming different distribution. I know some ways to do with for example normal dist. but it's not general for all pdfs.

2. Jul 17, 2012

### chiro

Hey re444 and welcome to the forums.

For a general distribution, if you know the PDF you can use things like Metropolis-Hastings for random number generation (pseudo-random) from that particular distribution. This is useful for a generic distribution that is completely non-standard.

For standard distributions, most software packages come with routines to do this for you. R is a very popular statistical package that is free and comes with a lot of packages. You can generate many random numbers from these distributions including exponential, gaussian, uniform, chi-square, poisson, binomial, and so on.

If you want to do something like say X/Y where X and Y are standard distributions then simply get a random number from both distributions and calculate the function (for example x = randomnumber1, y = randomnumber2, final random number = x/y).

That's the basic idea of doing the above. If you have a standard distribution, chances are there will be a function to generate it for you. If it's non-standard and you have the PDF, use something like Metropolis-Hastings.

3. Jul 18, 2012

### haruspex

The standard model theory approach is to pick a distribution that looks about the right shape for the data and has two or three parameters you can tune. You can then use maximum likelihood methods to tune it. You can try a few different distributions and compare them for likelihood, biasing against those needing more parameters. Standard methods for that biasing require the models to be "nested", which won't be true for rather different distributions, but I find the approach here http://en.wikipedia.org/wiki/Akaike_information_criterion persuasive.