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Expected value of the square root of a lognormal variable

The square root of a lognormal is itself lognormal. Indeed $Y^p$ is lognormal more generally. Note that if $X\sim N(\mu,\sigma^2)$ then $Y=\exp(X)$ is lognormal with the same parameters and vice versa....
Glen_b's user avatar
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15 votes

Expected value of the square root of a lognormal variable

If Wikipedia is trustworthy enough for you, it says that $$ E(X^n) = \text{exp}\big(n\mu+\frac{1}{2}n^2\sigma^2\big) $$ for real or complex $n$, so you can use this formula with $n=\frac{1}{2}$. ...
Stephan Kolassa's user avatar
1 vote

Suppose I am using KM curve to estimate S(t) parametrically (say assuming it follows lognormal)

The curve will be similar, but most months are a bit longer than 4 weeks, so a fit to t[weeks] will not be exactly the same as 0.25*t[months].
Niklas's user avatar
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6 votes

How is that possible that simple arithmetic mean works well even for strongly skewed distribution?

What is your definition about "good"? I assume you want to say the bias of sample mean is zero, it is consistent, if so, in 1947, Hsu and Robbins proved that the arithmetic mean converges ...
Tuobang Li's user avatar

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