# 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.

1,065 questions
Filter by
Sorted by
Tagged with
131 views

### Convergence of Step Functions Generated by Uniformly Distributed Random Points

I have encountered a surprisingly complicated problem to solve and I'm looking for some help. It could be difficult because I don't have a background in probability and so don't know the appropriate ...
12 views

23 views

### Order Statistics from a sum of exponential distributions

Let $X_i$ $(X_1, \dots, X_n)$ and $Y_i (Y_1, \dots,Y_n)$ be i.i.d. exponential r.vs with rate $\lambda$. Let $Z_i= X_i+Y_i$. How to write the pdf of the k-th order statistics of the $Z_i$ random ...
67 views

### Conditional Expectation when variables are drawn from uniform distribution of different domain

I have the following problem - $a$ and $b$ are independently drawn from uniform distribution. $a$ is drawn from uniform distribution $\{m, 1+m\}$ and $b$ is drawn from uniform distribution $\{0,1\}$. ...
9 views

### I want to choose the top 60% of animals in my study. 72% of the selection weight is due to random factors, while 28% is due to height.

I want to choose the top 60% of animals in my study. 72% of the selection weight is due to random factors, while 28% is due to their height (both random factors and height are in z scores and normal ...
• 5
21 views

### The probability of each specific ordering of a group of independent uniform random variables

Given: A sequence of $n$ positive real numbers (the scales of the uniform random variables) $t_1, t_2, \ldots, t_n \in \mathbb R_{+}$ Let: $x_1, x_2, \ldots, x_n$ be mutually independent uniform ...
• 2,098
26 views

### On the convergence in probability of the maximum statistic of a random variable according to triangular and uniform

Set up Consider the example in section 2 of Ferguson (1982). Let $X_1, \ldots, X_n$ be i.i.d. with a distribution which with probability $\theta$ is the $U(-1, 1)$, and with probability $(1-\theta)$ ...
• 564
1 vote
18 views

### 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 ...
• 597
27 views

24 views

### 6.36 of Theory of Point Estimation, second edition

the question is: $$X_1, X_2, ..., X_n$$ i.i.d random variables of uniform distribution U(a,b), where a<b. Show that $$Z_i = \frac{X_{(i)}-X_{(1)}}{X_{(n)} - X_{(1)}}$$ ,i = 2,...n-1, are ...
20 views

### Solving systems of simultaneous equations with permutations as variables: algebra meets combinatorics and order statistics

We may treat a given permutation as a vector variable, so that permutation s$_n$ is a variable that takes values among all possible number sequences of length $n$, which have elements in the rank ...
• 171
1 vote
39 views

### Fraction of the largest element of a sum of N i.i.d. random variates sampled from some distribution

I want to figure out how the fraction of the biggest sample of the sum of some iid samples from an arbitrary distribution varies. For example, I have a random variable $X \sim f(x)$, and I sampled $n$ ...
1 vote
60 views