Linked Questions
20 questions linked to/from Approximate order statistics for normal random variables
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Finding expected order statistics from a normal with known parameters [duplicate]
I'm interested in finding the expected value for the kth ordered observation of a normally distributed variable with known standard deviation, mean and n.
Could someone let me know the formula for ...
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Distribution of the top $m$ of $n$ samples of a Gaussian distribution? [duplicate]
I was wondering if there was an analytic description of the distribution of the largest $m$ of $n$ samples of a Gaussian distribution, where $n \geq m$.
(As an example, I generated 100 samples from $\...
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Distribution of maximum of normally distributed random variables
I'm trying to find the closed-form CDF and PDF of $Y = \max(X_1, ..., X_n)$ where $X_i \sim \mathcal{N}(\mu_i, \sigma^2)$.
My thought process so far:
$$
\begin{align*}
F_Y(y) &= \mathbb{P}(\max(...
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Expected value of maximum of samples from normal distribution
Lets say I have a normal distribution $N(\mu, \sigma^2)$ from which I have drawn $n$ i.i.d. samples $x_1, \dots, x_n$.
Now, lets define a random variable $Y = max(x_1, \dots, x_n)$.
When $n=1$, the ...
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Variance of Normal Order Statistics
Suppose we have $X_1, \cdots, X_n \overset{\textrm{i.i.d.}}{\sim} \mathcal{N}(0, 1)$ with $n > 50$, and let $X_{(1)}, \cdots, X_{(n)}$ be the associated order statistics.
Are there any references ...
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Explanation for this event on a high-dimensional dataset
Suppose we sample a set $S$ of $n$ points from a $d$-dimensional spherical (unit variance) Gaussian with $d \approx 100$. It is known that any point of the sample would be roughly at $\sqrt{d}$ ...
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What is the mean and variance of the median of a set of i.i.d normal random variables?
Let $X_1$, ..., $X_n$ be identically independently distributed random variables with $N(\mu, \sigma^2)$
It is easy to show that sample mean $\bar{X} = \frac{1}{n}\sum^n_{i = 0}{X_i}$ is a random ...
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Assuming two Gaussian distributions of equal mean and variance, then how different can we expect the top X members of each group to be?
Here's the thread I got the idea from: http://www.quora.com/Do-men-have-a-wider-variance-of-intelligence-than-women/answer/Ed-Yong
Basically, this is a model that might be able to explain why there ...
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Approximate variance for 99.5th percentile for normal distribution
My question is similar to this one:
Approximate order statistics for normal random variables
I am looking to find a formula for the variability of an arbitrary percentile of a normal distribution. ...
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In R, what does qqnorm actually do?
qqnorm(x)
plot(qnorm(seq(80)/81),sort(x))
Finding that the plots produced by the commands above are slightly different from each other, I tried this:
...
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Approximate Order Statistics for lognormal variables
Are there any known formulas that approximate the expected value of the maximum of $N$ i.i.d. lognormal random variables?
I am looking for something similar to:
Approximate order statistics for ...
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4
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expected lowest value of 10 normally distributed values
Consider 10 values that follow a standard normal distribution. What would you expect to be the lowest value?
I tried to simulate this problem in R. I basically just simulated 100000 standard normal ...
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Determine the limiting distribution of Standard Normal order statistics
Let $X_1,...,X_n$ be an i.i.d sample from the standard normal distribution. Is there any general formula for the first order statistic of this sample? For example, I have seen a formula by Blom (...
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Distribution of minimum distance in a iid Gaussian sample
$X_1,...,X_n$ denotes an iid sample with the same Gaussian distribution. I am interested in the distribution of the following quantity.
We first pick $i \in [n]$
Then we extract $j^* \in argmin_{j\...
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How to robustly present a min and a max value?
I have a set of measurements from an air polution sensor. I want to determine the min and the max value in a period of time (let's say in a day).
The min and the max don't have to be the true ...
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