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user9121
user9121
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I would like to know if there's a way to compute or approximate the following expectation:

$$\mathbb{E}[(c+e^X)^{-n}]$$

where $X=N(0,\sigma^2)$ and $n,c>0$ (you can also assume that $n$ is a natural number if necessary). After googling a bit I found the following articles: article1, 2 which talkstalk about negative moments of positive random variables but applying itthe methods yields a divergent series.

I would like to know if there's a way to compute or approximate the following expectation:

$$\mathbb{E}[(c+e^X)^{-n}]$$

where $X=N(0,\sigma^2)$ and $n,c>0$ (you can also assume that $n$ is a natural number if necessary). After googling a bit I found the following article which talks about negative moments of positive random variables but applying it yields a divergent series.

I would like to know if there's a way to compute or approximate the following expectation:

$$\mathbb{E}[(c+e^X)^{-n}]$$

where $X=N(0,\sigma^2)$ and $n,c>0$ (you can also assume that $n$ is a natural number if necessary). After googling a bit I found the following articles: 1, 2 which talk about negative moments of positive random variables but applying the methods yields a divergent series.

Source Link
user9121
user9121
  • 81
  • 2

Expectation of $(c+e^{N(0,\sigma^2)})^{-n},\, n>0$

I would like to know if there's a way to compute or approximate the following expectation:

$$\mathbb{E}[(c+e^X)^{-n}]$$

where $X=N(0,\sigma^2)$ and $n,c>0$ (you can also assume that $n$ is a natural number if necessary). After googling a bit I found the following article which talks about negative moments of positive random variables but applying it yields a divergent series.