- #1

tworitdash

- 108

- 26

When people assign a probability distribution to a variable in a physical process, is it inherently assumed that the parameters of this distribution are not related to each other?

My intuition says yes. If for example I assign a variable with a two parameter distribution and they are somehow dependent on each other, then it should be formulated as an one parameter distribution instead. Am I correct?

I have a similar situation in my research and I found in literature that the diameter of raindrops is gamma distributed with two parameters [itex] \eta [/itex] (shape parameter) and [itex] \Lambda [/itex] (inverse scale parameter - inversely proportional to the mean diameter in a volume). In old literature people really considered them to be independent parameters, but the current literature in this field show quite different results. When they try to fit it with gamma they really see a dependency of these two parameters.

This dependency can not be explained by any sort physical theory. Then, should the diameter be modeled by a different distribution instead?