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| ||<17%> ||<38%> $$\frac{i-0.3175}{n+0.365}$$ ||<45%> i=2, \ldots, n-1|| | ||<17%> ||<38%> $$\frac{i-0.3175}{n+0.365}$$ ||<45%> $$i=2, \ldots, n-1$$ || |
Quick formula for the expected value of a Normal order statistic
The expected value of the i-th Normal Order Statistic from a sample of size, n, may be computed as the absolute value of
$$\Phi^{-1}(U(i,n))$$
where $$\Phi^{-1}$$ is the inverse Normal cumulative density function which converts a probability, such as U(i,n), to a z-score.
where the U(i,n) are given as U(i) [http://en.wikipedia.org/wiki/Normal_probability_plot here.]
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U(i,n) |
i |
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$$ 1- 0.5^{1/n} |
i=1 |
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$$\frac{i-0.3175}{n+0.365}$$ |
$$i=2, \ldots, n-1$$ |
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0.5^{1/n} |
i=n |