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

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2
votes
1answer
215 views

SDE boundary condition

I have a simple SDE with white noise: ...
8
votes
1answer
203 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 ...
0
votes
2answers
194 views

Random variates in Recurrence Function

I'm completely new to Mathematica and can't seem to find an answer elsewhere so hopefully I can get some help here. I'm trying to plot a recurrence relation, where a random variate is generated at ...
2
votes
2answers
174 views

Bounds on random number

I have a Markov Chain Monte Carlo code that uses a chi squared function to fit some data. I am running into an issue now with getting unrealistic values for some of the free parameters in the code. ...
3
votes
1answer
615 views

White noise $\eta(t)$

How to make a random function $\eta(t)$ to insert in a differential equation for NDSolve? Edit: example: to solve equations like $\frac{dx}{dt}=\eta(t)$
1
vote
1answer
192 views

Safe values of $\mu$ and $\sigma$ when randomly sampling from a Log-Normal Distribution?

I believe I'm obtaining overflow errors when randomly sampling from a log-normal distribution with the command: RandomVariate[LogNormalDistribution[μ, σ], 1] ...
2
votes
0answers
534 views

Calculate variance of random walk?

How can I symbolically calculate the variance of the following random walk in Mathematica? Given several discrete random variables such that $p(Z_i=1-2k)=p$, where $k$ is a small real number, and ...
15
votes
1answer
627 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: ...
1
vote
2answers
267 views

Help with 1-dimensional random walk [closed]

I would like to simulate the evolution of a bankroll of a 2 player game where you have the probability of winning p. If a player wins, the bankroll grows by 1 unit minus a fee that each player pays, ...
12
votes
1answer
458 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 ...
2
votes
2answers
172 views

Illustrating half life

I'm teaching some lessons on negative exponents and one application listed was half life since the rate of decay can be written as 2^-1 every __ years. I found this nice animation on the net. ...
3
votes
2answers
276 views

Colors associated to parts of a 3D distribution of points

Suppose we have a long list of random points (cartesian coordinates) in 3D space. coords := ...; Until now, I was associating colors in a radial way, from the ...
2
votes
1answer
365 views

Radial Random Walk

I'm trying to generate a spherical distribution of radial random walk points in 3D space. The following code works, but the random walk lines aren't radial. Why ? Where is my mistake ? ...
1
vote
1answer
320 views

Gauss Markov Process

I am trying to model a 1st order Gauss Markov Process (gyroscope drift). I know the Allan Variance characteristics of the process (bias instability, random walk characteristics). I know the model ...
-1
votes
3answers
203 views

MixtureDistribution in Mathematica 7

Is it possible to use a mixture of several distributions in Mathematica 7.0? Consider for example the following code : ...
11
votes
3answers
539 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 ...
1
vote
1answer
278 views

How to reject or repulse some points in a 3D cloud of particles?

I'm having an issue with a 3D distribution of points. The distribution is really nicely looking in Mathematica, but it is used in an OpenGL astronomy program (Celestia) to generate a nebula, with ...
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. ...
6
votes
3answers
388 views

A deterministic function to generate a random number

Using Mathematica, I need to define a function of one integer variable that generates the same real number in the range 0 to 1, if it is called with the same argument, but gives a different real ...
19
votes
2answers
726 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 ...
14
votes
1answer
2k 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 ...
28
votes
1answer
963 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 ...
3
votes
3answers
546 views

Generating a random walk with defined step size

By the following I'm trying to generate a list of random coordinates (ex. 4) each within unit distance from previous one, starting from origin. What am I doing wrong? ...
7
votes
1answer
269 views

1D Random Walk with Excluded Sites and Variable Time-Step

Here is the physical problem I would like to simulate: Consider the following variations to the 1d random walk: allow for certain, random sites to be excluded with probability 1/2. allow for the ...
14
votes
3answers
615 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 ...
5
votes
1answer
335 views

Random number generation with specific distribution

I am writing a program for solving the shortest path in travelling salesman problem, with a twist that there are multiple salesmen who partition the cities among themselves, thus creating two part ...
1
vote
1answer
586 views

Add noise (random values) to data

I have a data set(x,y,z) corresponding to a hemisphere, to which I want to add some controlled noise (random values) to make the x,y,z values diverge. data = Flatten[ Table[{i, j, i^2 + j^2}, {i, ...
1
vote
1answer
318 views

Why does the mean in my coin tossing simulation not approach 1/2?

I simulate a simple experiment, a coin flip. What I do is accumulate the mean of the results up to the i-th experiment. What I can't figure out is why the computed means do not asymptotically approach ...
1
vote
1answer
157 views

Random sample with gap sizes

Lets say I have 101 instances of data with multiple attributes. In particular case, one attribute has 7 unique values. I want to get ...
8
votes
1answer
553 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 ...
13
votes
1answer
340 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: ...
16
votes
1answer
417 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: ...
1
vote
1answer
104 views

Draw from HistogramDistribution with ParallelTable

I wanted to check something, but ran into troubles using HistogramDistribution in combination with ParallelTable. The code does the following: Compute a HistogramDistribution of some sample and use ...
1
vote
3answers
414 views

Small random disturbance of a flat surface

I am trying to create an initial condition which is: 1 + 0.05 rand(x,y) Here rand is a pseudorandom function distributed in the interval (-1,1). This surface ...
15
votes
3answers
600 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 ...
2
votes
2answers
270 views

Generating a range of numbers according to some rules

I'm pretty new to Mathematica, and I'm mainly a programmer so I don't have a lot of knowledge about maths. I want to generate a set of UNIQUE incremental numbers (series) according to the following ...
1
vote
1answer
141 views

How to generate new random numbers in a Manipulate only on demand?

I was playing with a Manipulateto visually compare calculating the mean of Normal and Cauchy random data. ...
11
votes
2answers
459 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 ...
9
votes
2answers
555 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 ...
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 ...
2
votes
1answer
137 views

Randomizing a lab

I teach a class where students do a weekly lab in Mathematica. They do it in a computer lab, and because there are many of them, and only one of me, I encourage them to help one another. ...
9
votes
1answer
204 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 ...
6
votes
4answers
1k 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 ...
5
votes
4answers
2k views

How to generate random directed connected graph?

How to generate random directed connected graph? I need to create graph which will pass: ConnectedGraphQ[^]
8
votes
3answers
2k 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
5answers
1k 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?
14
votes
1answer
533 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 ...
9
votes
1answer
652 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 ...
2
votes
1answer
1k views

Creating a random normal matrix

I would like to create a random matrix with the constraint that the matrix must be normal, i.e. the matrix and its Hermitian conjugate must commute. I would create a random matrix "without ...
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 ...