# Linked Questions

0answers
239 views

### How does one choose a random isotropic direction and then have the vector have norm 1? [duplicate]

I want to choose a random vector in high dimensions such that it all directions have the same uniform chance (i.e. isotropic in all directions). My current idea is the following algorithm: sample v ...
0answers
113 views

### Why are IID normal random variables spherically symmetrical? [duplicate]

Given a finite sequence of $s+1$ IID normal random variables $X_1, \ldots, X_{s+1}$ They are spherically symmetrical. This means that the radial projection of the point $(X_1, \ldots, X_{s+1})$ onto ...
1answer
53 views

### Generate Uniform Random Variates with Constant Norm [duplicate]

How can one generate $k$ uniform random variates centered at zero, $X_1, X_2, ..., X_k$, given a constant Euclidean norm, $c =\sqrt{X_1^2+X_2^2+...X_k^2}$?
4answers
19k views

### How to create an arbitrary covariance matrix

For example, in R, the MASS::mvrnorm() function is useful for generating data to demonstrate various things in statistics. It ...
3answers
14k views

4answers
507 views

### Creating random points in the surface of a n-dimensional sphere

I have a point X in the surface of an n-dimensional sphere with center 0. I want to create random points following a distribution with center X, the points must be in the surface of the n-dimensional ...
1answer
7k views

### How to use Box-Muller transform to generate n-dimensional normal random variables

I'm trying to generate random variables. I read about Box-Muller transform which is a way to generate a pair of normal variables, 2-d normal distrubution. But how do I expand that transform to ...

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