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12
votes
4answers
298 views
Unbiased estimator for the smaller of two random variables
Suppose $X \sim \mathcal{N}(\mu_x, \sigma^2_x)$ and $Y \sim \mathcal{N}(\mu_y, \sigma^2_y)$
I am interested in $z = \min(\mu_x, \mu_y)$. Is there an unbiased estimator for $z$?
The simple estimator ...
6
votes
3answers
4k views
How is the minimum of a set of random variables distributed?
If $X_1, ..., X_n$ are independent identically-distributed random variables, what can be said about the distribution of $\min(X_1, ..., X_n)$ in general?
