Talk:Compound probability distribution
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Exponential-inverse gamma
[edit]The article contains the text "Compounding an exponential distribution with parameter distributed according to an inverse gamma distribution yields a pareto distribution." I am not sure this works and https://math.stackexchange.com/questions/646852/compound-of-gamma-and-exponential-distribution suggests that it should be an exponential-gamma mixture. I don't have a reference for this though. 217.44.78.244 (talk) 07:52, 27 September 2016 (UTC)
The proof is muddled
[edit]In the subsection Proof, there are unnecessary and confusing simplifications and misleading or mistaken notation.
1) There is no good reason to write and as if they are parametrized by mean and standard deviation. In fact, it is misleading, because we are given only that is parametrized by , and is fixed. The other three quantities are outcomes, not parameters.
Furthermore, there is no reason to assume that the relation between and is bijective, so reparametrization to make them equal might not be possible.
2) Writing the variance as is incorrect, since is a random variable and is a constant. (If it is intended to be a random variable, this has not been declared, and moreover, it can't be pulled out of an integral as the quantity is.)
It would be better if
a) The expression were substituted for wherever the latter is being used to denote the mean of , and
b) The variables , , and were deleted, and replaced by the expressions
- .
In fact, these quantities are all calculated at some point in the proof as it is written, so the logic and sequencing of the proof don't have to change, just the symbols in the calculations.
2A02:1210:2642:4A00:C9E4:9F6:5E99:526E (talk) 20:07, 23 June 2023 (UTC)