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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. Order statistics are widely used in non-parametric inference.

This tag is for questions about order statistics and for questions in which one wants to calculate a probability, expected value, variance, standard deviation, or similar quantity of 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. Order statistics are widely used in non-parametric inference, methods which avoid assuming the form of distribution of the population from which a sample is drawn.

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First and second order statistics

In this paper Boltzmann Machines, the first paragraph of the second section 2. Boltzmann Machines argues that, we could never train such a network with three units to visit the states (0,0,0), (0,1,1), (1,0,1) and (1,1,0) with some…
Jiang Xiang
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Expected value of order statistics

Let $X$ be a non-negative random variable distributed on $[a,b]$ where $0
Learner
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Order Statistics Example : Electronic components of a certain type...

Electronic components of a certain type have a length life (in hours) X, that follows the exponential distribution with probability density given by $$f(x) = \frac{1}{100}e^{-x/100}, x > 0 $$ a. Suppose that 2 such components operate independently…
user3325193
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Formulating an order statistics problem

I've done some googling, but there are a few different notations employed, and I don't feel I've found an answer I'm comfortable with. Suppose you have a sample of 'i.i.d' observations $X_1,\dots,X_n\sim f$, and want to take an expectation…
jameselmore
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Looking to create a ranked list for PUBG teams

PUBG is a video game played with multiple teams in each game. I am looking to create a rating system so that as teams play each other, they will gain/lose rating based on their placement (1st being the best), how many teams were playing (making it…
Colton Berkley
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Three part question

According to Labor Statistics, 75% of the women 25 through 49 years of age participate in the Labor force. Suppose 78% of the women in that age group are married. Suppose also that 61% of all women 25-49 years of age are married and are…
Janet S.
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Revisiting the distribution of mth order statistic using symmetry

Not asking for the distribution of $m$th order statistic, for it has been well documented and covered and in fact well-known. What I am rather confused, perhaps basic but failing to see, is the approach using the argument of symmetry in the book, An…
User1865345
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Percentile using subsets percentile

IS there a way to calculate overall percentile of a set using its subsets percentiles? Assuming a set of made of smaller subsets, with each subset known number of values and known percentile.
fmvpsenior
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Joint distribution of top order statistics of two independent random samples

Suppose $X_1,...,X_n$ and $Y_1,...,Y_n$ are all independent copies of a standard Pareto random variable. For each of the 'two' random samples we can denote the order statistics $X_{n:n} \geq X_{n-1:n} \geq \ldots \geq X_{1:n}$, and, $Y_{n:n} \geq…
Joogs
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Can order statistics be a random samples?

We can say a random sample means that $ X_1, X_2, \ldots , X_n $ are iid from a same distribution. But Can we use a same analogue to order statistics? I mean, Can we convert $ X_1, X_2, \ldots , X_n $ to order statistics $ Y_1, Y_2, \ldots, Y_n $…
Minho Kang
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Order Statistics $P(X_i|X_{(j)})$

Let $X_1,...,X_n$ be an i.i.d. sequence and $X_{(1)},...,X_{(n)}$ be the order statistics. Assume that $X_i$ is uniform on $[0,1]$. Question: How to compute the distribution \begin{align} P(X_i|X_{(j)}) \end{align} My attempt: First Approach:…
Lisa
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Sufficiency with order statistics

What if we need to look for a sufficient statistic. We do the maths and we end up with a specific formule (with help of the factorization criterion) and we have the random variables X,i bounded; 0 < X,i < THETA. Which can be written with order…
Salim
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distribution of order statistic from dependent and independent variables

Consider $X_1$, $X_2$, $X_3$ and $X_4$ are four variables, we know that $X_1$ and $X_4$ are dependent $(X_1 < X_4)$, and $X_2$ and $X_3$ are dependent $(X_2 < X_3)$. Here $X_1$ and $X_2$ are independent, similarly $X_3$ and $X_4$ are independent…
Abdul Haq
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Intuitive approximation and Order Statistics

Given $x_1, x_2, \dots, x_n$ identically distributed random variables with probability density and cumulative distribution functions $f$ and $F$ respectively, the probability density function for the maximum is $$ f_{max} \big(x_{max} (x) \big) =…
An aedonist
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Conditional covariance of functions of order statistics

Suppose I have $n$ independent, non-identically distributed random variables $X_1, X_2, ..., X_n$. Let $\mathbf{X}$ denote the corresponding random vector with joint density $f(\mathbf{X})$ simply the product of the individual densities. Let…
orderstats
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