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

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34
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3answers
1k views

Quality of random numbers

Mathematica has several ways of generating random numbers: Congruential, ExtendedCA, Legacy, MersenneTwister, MKL, ParallelGenerator, ParallelMersenneTwister, Rule30CA. For ...
33
votes
5answers
2k views

Distribution of random points in 3D space to simulate the Crab Nebula

I'm generating some 3D models of planetary nebulae and supernova remnants for Celestia, a free OpenGL astronomy software. Currently, I know how to do it with random points inside a spherical shell. ...
27
votes
2answers
2k views

Efficient Langevin Equation Solver

This question is not about good algorithms for solving stochastic differential equations. It is about how to implement simple codes in Mathematica efficiently exploiting Mathematica's programming ...
25
votes
6answers
2k 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 ...
25
votes
1answer
752 views

Finding the likeliest path in a Markov process

With Mathematica 9, we have the addition of various processes, among which the discrete Markov process. Given a transition probability matrix m, such a process is ...
23
votes
1answer
1k views

RandomVariate from 2-dimensional probability distribution

A probability distribution can be created in Mathematica (I am using 8.0.1) with e.g. ...
22
votes
4answers
406 views

obtaining random element of a set given by multiple inequalities

I try to obtain random elements from a set given by multiple inequalities. This is of general interest to me, but let me present one example here: I have multiple inequalities specifying half spaces ...
19
votes
2answers
600 views

Efficient Generation of Random Variates from a Copula Distribution

I have a 7-asset portfolio for which I want to simulate daily log-deltas using a Student T copula. The marginal distributions are all either Stable or TsallisQGaussian. Using NMaximize, I have ...
16
votes
4answers
1k views

Efficiently generating n-D Gaussian random fields

I am interested in an efficient code to generate an $n$-D Gaussian random field (sometimes called processes in other fields of research), which has applications in cosmology. I wrote the following ...
16
votes
1answer
377 views

Simulating Theatre puzzle

I have been trying to simulate the process of the theatre puzzle from the Joy of X (Strogatz). The puzzle, and some relevant material are here. My simplistic coding for this process follows: ...
15
votes
8answers
376 views

Is it possible to use RandomChoice to choose without other choices being evaluated?

I'm trying to do this: i1 = 1; i2 = 1; RandomChoice[{ (i1 = i1 + 1), (i1 = i1 - 1), (i2 = i1 + 1), (i2 = i2 - 1)}] In order to chose randomly which ...
15
votes
4answers
944 views

Random data generator

Inspired by Quality of random numbers I would like to set up a true random data generator in Mathematica. My idea is to use the static from an open microphone. I recall reading about extracting the ...
15
votes
3answers
500 views

Plotting the solution of a vector stochastic differential equation

I have a vector stochastic differential equation, $$\mathrm dq = p\,\mathrm dt\qquad q(0)=0$$ $$\mathrm dp = (-q -p)\mathrm dt+\mathrm dW\qquad p(0)=10$$ This can be entered to give me the process ...
14
votes
3answers
731 views

Finding the volume of a sphere using the Monte Carlo algorithm

I used the following code to find the volume of the sphere $x^2+y^2+z^2 = 1$ in the first octant: ...
14
votes
5answers
735 views

Picking random items out of a list only once

I'm trying to create a function that randomly returns a value from a list but remembers the values that have been given before. At the end when the list is empty it should return an empty list. ...
14
votes
1answer
581 views

Mathematica giving infinity as a random number!

I am trying to generate several random numbers from normal distribution using Mathematica. The following is the relevant code: ...
14
votes
1answer
473 views

Simulating Stochastic Processes the MMA way

This question is really a specific problem and a methodological one concerning MMA best practices. I want to simulate a system of stochastic processes. If this were a geometric Brownian motion or ...
14
votes
1answer
269 views

Making Monte Carlo simulation with ParallelTable

I would like to to MonteCarlo simulations of various regressions - basically, doing OLS under various conditions to test approaches. On my macpro 2x 2.8 GHz quad core Xeon, 32 Gb RAM DDR2 @ 667 Mhz, ...
14
votes
1answer
1k views

Compare C++ Standard Library's Mersenne Twister with Mathematica's Mersenne Twister

The C++ standard library does contain a set of random distribution classes, among other things a Mersenne Twister engine. What I'd like to do is to generate the same random number distribution, using ...
13
votes
3answers
580 views

Generate a Random Polygon

Does some package exist with a function that takes a parameter $n$ and generates a random 2D $n$-sided simple polygon (convex or non-convex), possibly within a certain bounding box? It does not ...
13
votes
1answer
330 views

RandomVariate returns values outside the support of a PDF

Let $X$ be a random variable with pdf: dist = ProbabilityDistribution[1/(Abs[x]*Log[Abs[x]]^2), {x, -E^-2, E^-2}] Here are some pseudo-random drawings from it: ...
13
votes
1answer
424 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 ...
12
votes
1answer
393 views

Simulating discrete time stochastic dynamic systems

What is the canonical way of simulating discrete time stochastic dynamical systems in Mathematica using the new functionality of Random processes? To take a concrete example, lets consider the ...
12
votes
1answer
176 views

Randomness test suites that can be invoked from Mathematica

There are several test suites referenced at csrc.nist.gov designed to test a (pseudo-)random byte sequence for randomness, and discover possible skews, correlations, patterns, or other hidden ...
11
votes
3answers
446 views

Efficient implementation of a linear complexity measure of binary sequences

For a implementation of testing the quality of random number generators I implemented the NIST test suite in Mathematica based on the nice workbook by Ilja Gerhardt. However I took up the challenge ...
11
votes
1answer
269 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 ...
10
votes
2answers
403 views

Fast Simulations with Compile

this post relates to another post that I didn't follow up propely. If I wanted to simulate a system of stochastic proesses like the following, and loop over this run many many times would writing the ...
10
votes
3answers
504 views

1D Random Walk variant

I am making a notebook that is a variation to the traditional 1d random walk problem. The normal 1D random walk can be simulated easily by ...
10
votes
2answers
492 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 ...
9
votes
4answers
295 views

Why is Poisson Random Deviate Generation so slow?

I am generating Poisson deviates for some numerical work. Mathematica 9.0.1 is very slow in generating these random numbers, as can be seen below. ...
9
votes
3answers
2k views

How to generate a RandomVariate of a custom distribution?

I'm trying to generate a pseudorandom variate out of a custom distribution. Suppose I want define a custom distribution, and for the sake of simplicity I define a Poisson distribution (the ...
9
votes
1answer
576 views

Functional programming and Do loops

I'm writing a Monte Carlo simulation. I'm using a Do loop to create the different simulations, iterating over different ...
9
votes
1answer
180 views

RandomReal closed on left & open on right?

I have a number of algorithms that depend on uniform random reals in half-open intervals such as $[0,1)$. In particular, I need a (pseudo) random-number generator that produces machine-precision ...
8
votes
3answers
365 views

Create sine function with random increase in phase

I am trying to simulate a signal that randomly increases its phase, so far I have tried two thing but neither worked. I usually use matlab but I want to learn some Mathematica so I thought I would try ...
8
votes
2answers
485 views

Fluorescence Correlation Spectroscopy Simulation

I am simulating Fluorescence Correlation Spectroscopy which basically involves tracking the random motion of particles in a box with periodic boundary conditions and then calculating their intensity ...
8
votes
2answers
442 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 ...
8
votes
1answer
187 views

Have the Random functions changed?

I re-ran a program I wrote for Mathematica v8, now on v9, and it appears to generate different RandomInteger numbers, even though I use the same ...
8
votes
1answer
345 views

Uniformly distributed n-dimensional probability vectors

What's the right way to generate a random probability vector $p={p_1,\ldots,p_n} \in {(0,1)}^n$ where $\sum_i p_i=1$, uniformly distributed over the $(n-1)$-dimensional simplex? What I have is ...
8
votes
1answer
510 views

Recommended book on random processes to understand new functionality in Mathematica 9?

I am interested in exploring the new functionality on random processes available in Mathematica 9, but I am not familiar with all of the underlying mathematics. Could you recommend a book that ...
7
votes
2answers
562 views

How could I generate words starting with P,h,D?

A friend of mine is a PhD candidate and posted a picture on Facebook with funny words starting with 'p', 'h' and 'd' like "Please hire. Desperate" or "Permanent head Damage". I thought I could try and ...
7
votes
2answers
164 views

Counting and extracting hit circles/triangles for randomly chosen points

Below, you see a triangle in which the incircle was inscribed. As we know, the center of this circle is the intersection of the angle bisectors. At this point, one could go further and find the ...
7
votes
1answer
760 views

Wald–Wolfowitz Runs Test

Does Mathematica 8 implement Wald–Wolfowitz runs test for randomness? I can't find it in the documentation. I would like to test some fit residuals.
7
votes
3answers
1k views

Randomly packing spheres of fixed radius within a cube

How can I have Mathematica randomly place spheres in a cube so they won't overlap? The cube is $20 \times 20 \times 20$, and the spheres have a radius of $0.7$.
7
votes
1answer
260 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 ...
7
votes
1answer
102 views

Inconsistent DistributionFitTest results?

In pondering this question, I used Mariana's function to generate the following data. ...
6
votes
5answers
904 views

Vectors with a certain magnitude in Mathematica

For a user specified magnitude, is there a way to have Mathematica produce any 3D vector that fits that magnitude?
6
votes
4answers
873 views

3D Random Walk with Periodic Boundary Conditions

I am working on a 3D random walk with periodic boundary conditions and have written a program that will do this for me but it is extremely slow. Does anyone have any suggestions on how I could speed ...
6
votes
3answers
971 views

Generating unique random number lists

I am new in programming. I have an array containing, let's say 20 elements and first I want to randomly select two elements from it and record them. Then I will select two elements from the array of ...
6
votes
3answers
423 views

How to randomly erode a 3D distribution of points with Mma 7.0?

Suppose we have a 3D distribution of points, like the spherical ball example below : ...
6
votes
2answers
82 views

Algorithm in RandomChoice[{w1,w2,…}->{e1,e2,…},n]?

I wonder if someone happens to know the actual algorithm implemented in the particular overload of RandomChoice that handles explicitly presented discrete ...