Questions about random number generation and the properties of numbers so generated.

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39
votes
3answers
2k views

Quality of random numbers

Mathematica has several ways of generating random numbers: Congruential, ExtendedCA, Legacy, MersenneTwister, MKL, ParallelGenerator, ParallelMersenneTwister, Rule30CA. For ...
7
votes
1answer
338 views

RandomVariate with a Discrete Distribution

Nature has provided me with a random variable $Z$ taking on the values $0, 1, 2, \ldots$, with probabilities $z_0, z_1, \cdots$. I can sample from the distribution of $Z$ reasonably efficiently (I ...
9
votes
2answers
599 views

Most efficient way to obtain samples from high-dimensional multivariate distributions?

Is MultinormalDistribution[] efficient and easy to use for high dimensions? I have a variable $n$ representing the dimension of a Monte Carlo integration I do on a ...
-11
votes
4answers
492 views

Going Beyond Pseudorandom Numbers

I cooked up this simple bit of code in hopes to exceed pseudorandom number generation maybe touch the face of true randomization: ...
30
votes
1answer
2k views

RandomVariate from 2-dimensional probability distribution

A probability distribution can be created in Mathematica (I am using 8.0.1) with e.g. ...
31
votes
7answers
3k views

Efficient way to generate random points with a predefined lower bound on their pairwise Euclidean distance

Using Mathematica what is an efficient way to generate a list of $n$ random two dimensional points $\{x_i,y_i\}$ where $i=1,...,n$ so that no two points $p_1$ and $p_2$ in the list has an Euclidean ...
12
votes
1answer
342 views

Are there rules of thumb for knowing when RandomVariate is more efficient than RandomReal?

Please consider the following: From a fresh Mathematica kernel, RandomVariate is more efficient for NormalDistribution but ...
4
votes
1answer
315 views

How to fix errors in Gram-Schmidt process when using random vectors?

I first make a function to get a random vector on unit sphere in a swath around the equator. That is what the parameter $\gamma$ controls; if $\gamma = 1/2$, the vectors can be chosen anywhere on the ...
7
votes
2answers
534 views

Generate Random Text within a Rectangle

I would like to generate images such as the four below. That is: some text of different length fit within a Rectangle[] using ...
3
votes
2answers
1k views

creating vectors with normal distribution of lengths

First consider vectors of unit length, say on the unit sphere. Now I want to give some magnitude to these vectors and I want the magnitude to be chosen from the normal distribution. In one dimension ...
10
votes
2answers
622 views

Creating randomly oriented planes

I would like to create randomly oriented planes. This is how I'm attempting to do that: I create a 2 random unit vectors, $\mathbf{v}_1$, and $\mathbf{v}_2$, in the $x$-$y$ plane I assume that if I ...
3
votes
1answer
180 views

Generate a new output using Manipulate

Thanks to methods found in the below, I was able to assemble those elements : Tile image on specific location without space between them How to combine images with the same dimensions in a grid? ...
24
votes
3answers
851 views

Which Distributions can be Compiled using RandomVariate

Recently, Oleksandr kindly showed a list of Mathematica commands that can be compiled. RandomVariate was part of that list. However, whether this can be compiled depends upon the distribution that is ...
15
votes
3answers
4k views

How to generate random directed acyclic graphs?

How to programmatically build random directed acyclic graphs (DAG)? I know about the AcyclicGraphQ predicate and the ...