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In a sum of high-variance lognormals, what fraction comes from the first term?

Let's start with $Z_i \overset{\textrm{iid}}{\sim} \text{Normal}(0, 1)$ and let $X_i=e^{\sigma Z_i}=\left(e^{ Z_i}\right)^\sigma$ and $Y_i = X_i / \sum_{j=1}^n X_j$. With probability $\frac1n$, $Z_1= ...
Henry's user avatar
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3 votes
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Approximation of the expected value of the $i$-th standard normal order statistic in a sample of size n

Here is an example of using numerical integration to find the expected values using Mathematica which is more accurate than Blom's equation. (Note: to make a "nice" table there are ...
JimB's user avatar
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