Questions tagged [uniform-distribution]
The uniform distribution describes a random variable that is equally likely to take any value in its sample space.
867 questions
8 votes
1 answer
91 views
How to uniformly sample from a nonlinearly transformed simplex?
Let $S = \{ w \in \mathbb{R}^3 : w_1 + w_2 + w_3 = 1,; w_i \ge 0 \}$ be the standard 2-simplex. Consider the transformation $$ T(w_1, w_2, w_3) = (w_1, w_2^p, w_3), $$ not followed by a ...
2 votes
0 answers
68 views
Dependence structure of inner products of vectors on unit sphere
This relates to the question here Distribution of scalar products of two random unit vectors in $D$ dimensions but I don't have enough reputation to ask this as a comment... anyway. The reply to the ...
- 31
7 votes
1 answer
143 views
Transform convex hull vertex weights for uniform distribution
Given an $n$-dimensional convex hull implied by $m$ vertices $V$, $m \approx 40$, $3 \le n \le 10$, I want to generate $p$ random points that are contained in the hull and are as uniformly-...
- 285
0 votes
0 answers
47 views
Cdf of sum of two uniform random variables [duplicate]
Let $ X \sim U[m,M] $ and $ Y \sim U[b,B] $, meaning their probability density functions (PDFs) are: $ f_X(x) = \frac{1}{M - m}, \quad m \leq x \leq M $ $ f_Y(y) = \frac{1}{B - b}, \quad b \leq y \leq ...
- 1
4 votes
1 answer
77 views
Sampling from a multinomial distribution with K categories by sampling K independent uniform distributions and sorting
Consider a multinomial distribution with $K$ categories, where each of the categories has a probability $p_k, k\in \{1,...,K\}$ of being selected in a random trial such that $\sum_{k}p_k=1$. In ...
- 41
1 vote
1 answer
111 views
Ratio of a uniforms distributions variables in $\left\{ (u, v); 0 \leq u \leq \sqrt{\tilde{\pi}(v/u)} \right\}$ is distributed $\pi$
Problem: Let $\pi = \tilde{\pi}/Z_\pi$ be any probability density function on $\mathbb{R}$. Prove that if $(U, V)$ is uniformly distributed on $G = \left\{ (u, v); 0 \leq u \leq \sqrt{\tilde{\pi}(v/u)}...
0 votes
0 answers
32 views
Estimating the pdf of a set of variables
I have the following subproblem I'm working on. I am given a complete weighted graph, $G = (V,E)$. The set of edges $E = \{X_{uv}\}$ for $1 \leq u < v \leq n$ is a set of random variables where ...
- 11
0 votes
0 answers
33 views
Independency in samples removal
I have the following subproblem I'm working on. I am given a complete weighted graph, $G = (V,E)$. The set of edges $E = \{X_{uv}\}$ for $1 \leq u < v \leq n$ is a set of random variables where ...
- 11
0 votes
0 answers
99 views
Transforming a distribution where the order matters
I have a set $E = \{X_{ij}\}$ for $1 \leq i < j \leq n$, s.t. $|E| = \binom{n}{2}$. The $X_{ij}$ are all i.i.d. in $\sim [0,1]$. These are the edges of a complete weighted graph. Suppose I pick a ...
- 11
1 vote
0 answers
130 views
Uniformity of probability distribution
I have a question concerning the removal of samples from a set of uniformly distributed samples. Let $E = \{ X_{ij} \}, 1 \leq i < j \leq n$ be a set of random variables where each $X_{ij}$ is i.i....
- 11
7 votes
2 answers
350 views
Do scaled-down integer lattice points serve as unbiased sample points in the probability simplex?
I'm stuck trying to prove a statement that seems intuitively obvious but not really straightforward to establish rigorously. The $(n-1)$-dimensional probability simplex $X$ is the set $$ X=\left\{\...
- 223
0 votes
0 answers
60 views
Can orthogonality of features be established by observing changes in the loss function?
Say I have a regression or classification problem and collect a large amount of data. My hypothesis is that if I choose $2$ orthogonal (or perhaps orthonormal?) features, then each feature should ...
- 133
2 votes
1 answer
181 views
Confidence interval for ${θ}/{2}$ in $\text{U}(0, \theta)$
I am trying to find a confidence interval for ${\theta}/{ 2}$ with confidence level $1-\alpha$ (using quantiles at $p_1 = \alpha$ and $p_2 = 1$). So I take unbiased estimator for ${\hat{\theta}}/{2} =...
- 123
1 vote
0 answers
111 views
Can anyone think of a real situation in which the parameters of a uniform distribution need to be estimated?
(now with edits based on the responses) I'm looking at the question of how to predict values from the continuous uniform distribution, based on samples from a continuous uniform distribution with ...
- 199
9 votes
1 answer
455 views
Defining a uniform distribution over the perimeter of a polygon
Problem definition Consider a polygon with vertices $V_1,\dots,V_n \in \mathbb{R}^2$ and let \begin{equation*} \begin{aligned} z&=\underbrace{\sum_{j=1}^n \left[(V_{j+1}-V_j) \frac{L}{L_j}\left(\...
- 473