# 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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### Is there a function that yields the "sorted" PDF of a distribution? [closed]

I am implementing a program where I'd like to compute the indices of the most likely values in a vector where the PDF is known, in descending order. It could be done by discretizing and sorting the ...
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### Jacobian of function returning $m$ evenly-spaced order statistics of an $n$-dimensional vector

Let $y\in\mathbb{R}^n$, and let $f:\mathbb{R}^n\to\mathbb{R}^m$ be the transformation that outputs $m$ evenly-spaced order statistics (including the extremes) of $y$. What is the Jacobian of this ...
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### Probability of two people being born within the last 200,000 years and within 5 years of each other

I've come up with the number that there's a 1/30 Sextillion chance of being born on Earth. That's considering that you will be born and that there are 30 Sextillion potential planets that could be ...
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### Probability that a normal RV is greater than multiple other normal RVs

Let $X_1, X_2, ... X_n$ be independently drawn from different normal distributions, such that $X_i \sim N(\mu_i, \sigma^2_i)$ For any $j$ what is the probability that $X_j$ is the greater than all ...
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### PDF of the linear combination of two order statistics

I have just started to learn order statistics so please feel free to correct my notation/terminology. In my field is common to provide data as the median of some sample (for example several ...
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### Nonparametric Order Statistics - Does this Exist?

I was reading about Order Statistics (https://en.wikipedia.org/wiki/Order_statistic) : Apparently, if we have a sample with "k" number of elements (e.g. x1, x2, ...xk) and assume a ...
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### Statistical test for low treatment sample size, high nb of record and large control group

I am looking to analyse the efficiency of a treatment. The problem is that I have only 3 patients in the treatment group. However: I have thousand of measurement of the value of interest for these 3 ...
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### Boolean order statistic

Inspired from this LeetCode question. I authored this question myself however. Please review my answer for accuracy. Let's sort an array ($n \ge 1$) of $1$s and $0$s, so that all $0$s come before $1$s....
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### Calculate how many defective parts with p=0.95

After a 2 month test, there is a result of 5 defective parts out of the total sample size of 50 tested parts. How many defective parts can be expected for an annual production of 70000 parts (p=0.95)? ...
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