# Questions tagged [order-statistics]

The order statistics of a sample are the values placed in ascending order. The i-th order statistic of a statistical sample is equal to its i-th smallest value; so the sample minimum is the first order statistic & the sample maximum is the last. Sometimes 'order statistic' is used to mean the whole set of order statistics, i.e. the data values disregarding the sequence in which they occurred. Use also for related quantities such as spacings.

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### Estimate population mean from "best of N" samples

If I have a data set for which I know all measurements represent the largest of N observations, is there a good method for estimating the mean of all observations? So for example if N=10 and I have 3 ...
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### computing $P\left(\max(U_{(1)}, U_{(2)}-U_{(1)}, \cdots,U_{(n)}-U_{(n-1)} ) <a\right)$

Let $U_{1}, \, ... \, ,U_{n}$ be a random sample of uniform random variables $U_i \sim \mathrm{Uniform}(0,1)$. Let $U_{(1)}, \, ... \, , U_{(n)}$ be the order statistics of the sample. My problem is ...
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### What are E(max(X1, X2)) and Var(max(X1, X2)) when the Xs are normal random variables? [duplicate]

Let X = (X1, X2) be normally distributed random variables with mean m = (m1, m2) and covariance matrix S. Y = max(X1, X2) = X1 + max(0, X2 - X1) = X1 + D (X2 - X1), where D = 1 if X2 > X1 and 0 ...
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### exponential parameter estimtion from the smallest k-th order statistics

Assume $X_1, X_2, X_3,\ldots,X_n$ are i.i.d. samples from Exp($\lambda$). Assume that the integer $k<n$, is it possible to find a an unbiased estimator for $\lambda$ from the k-th smallest ordered ...
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This question came up based on a disagreement I had with a TA. This was the specific example: Let $X_{1},...,X_{n}$ be an iid random sample from a population with pdf $f(x)=3(1-x)^2, 0<x<1$. The ...