I have a dataset containing daily rainfall values which has some zero values in it. Can i fit lognormal, exponential, gamma, beta distributions to this? How to do so stepwise?

I have a dataset containing daily rainfall values which has some zero values in it. Can i fit lognormal, exponential, gamma, beta distributions to this? How to do so stepwise?

Answer 1

[Walter Roberson]

• lognormal: NO, the log(0) will ruin the calculations
• exponential: NO unless it is exponential plus constant rather than pure exponential. Exponential can only exactly equal zero at -infinity
• gamma: NO, gamma(0) is infinity and that will ruin the calculations
• beta: the PDF for the beta distribution at the (fixed) lower bound should be 0, and you will have a non-trivial number of 0's, leading to a PDF at your zero samples that is distinctly non-zero. Beta is not going to fit well. Also, beta distribution requires a fixed upper bound, but rainfall distribution does not have a fixed upper bound. You could, I suppose, use 1.825m as your fixed upper bound (Reunion Island, 1966), but with climate change it is far from certain that will remain the record. I don't think you could possibly get a reasonable beta distribution with that kind of long tail.