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I would like to calculate the expectation of the minimum value among a Poisson-distributed-number-of-draws from a normal distribution.

Appreciate some guidance in formulation of the expectation.

Below is a derivation where n is deterministic (not distributed by Poisson)

Expectation of minimum of $n$ samples from Gaussian distribution

user152112
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  • Did you mean minimum of the Poisson-distributed-number-of-draws and a normal distribution? – Cem Sarıer Jan 02 '18 at 12:19
  • I effectively want an expression for the "expected extrema" similar to https://mbhs.edu/~ansarma/stat.pdf, but rather than N (num of draws) being deterministic, it itself follows the Poisson distribution. – user152112 Jan 02 '18 at 12:30
  • Can you find an expression for $f(n):=\mathbb E\min(U_1,\dots,U_n)$ where the $U_i$ have standard normal distribution? If so then proceed with calculation of $\mathbb Ef(N)$ where $N$ has Poisson distribution. Note that you must provide a default for $f(0)$. – drhab Jan 02 '18 at 12:48
  • Well I can (link above, and another here) but deriving an extension of this where n is poisson-distributed is not trivial ... how would you suggest to "proceed with calculation"?https://math.stackexchange.com/questions/2584779/expectation-of-minimum-of-n-samples-from-gaussian-distribution?rq=1 – user152112 Jan 02 '18 at 13:20

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