Basin-volume notes

probability distribution

The end result of this project will be a series of volumes sampled from an unknown probability distribution. We want to determine what that distibution will be. We will have a functional form for that distribution \(P(V | \theta )\) where \(\theta\) are the unknown parameters of the distibution. In the past we’ve used a generalized Gaussian. \(P(V | \theta)\) is the biased distribution, so it will be the generalized gaussian times \(V\). This is mostly taken from http://en.wikipedia.org/wiki/Distribution_fitting

There are several ways to determine what the values of \(\theta\) should be. None of which involve histogramming.

maximum likelihood method

http://en.wikipedia.org/wiki/Maximum_likelihood

The likelihood is the joint probability distribution of all the observations given the set of parameters