Hi, This is a conclusion of my previous post on how to get the expectation and variation of a ratio. I've received many suggestions, thanks to all your guys!
1) I still did not figure out what is in the wiki method ( http://en.wikipedia.org/wiki/Taylor_expansions_for_the_moments_of_functions_of_random_variables), but it should be something related to delta method. 2) It is also possible that the distribution of a ratio is infinite, according to this (http://en.wikipedia.org/wiki/Ratio_distribution). 3) There is one solution in a 1993 book by Buckland (Distance Sampling). In page 52 - 53, he provided an equation to estimate the variation of a ratio. It needs sometime to realize that he is actually talking what I need out of the math jargon. So I found another paper, by Cox, 1990, Fieller's Theorem, the Likelihood and the Delta Method. In page 711, you can find a nice equation on how to do this. There seems to be some assumptions, but we are dealing with ecological data, so no a big deal I think. I want to thank David for his suggestion on Buckland's book and method. Hope this would help. Cheers. Zewei Song University of Minnesota
