# Tagged Questions

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

0answers
51 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. ...
1answer
141 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 $\frac{dx}{dt}=\eta(t)$
1answer
98 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] ...
1answer
143 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 ...
1answer
447 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: ...
2answers
114 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, ...
1answer
174 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 ...
2answers
132 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. ...
2answers
138 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 ...
1answer
166 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 ? ...
1answer
129 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 ...
3answers
146 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 : ...
1answer
243 views

### Distribution of random points in 3D space to simulate an Orion-like Nebula [closed]

I'm creating 3D nebulae models for Celestia, a free OpenGL astronomy software. The following question is in part related to another one I already asked on this forum (see this question, for which I ...
3answers
237 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 ...
1answer
151 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 ...
5answers
984 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. ...
3answers
224 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 ...
1answer
286 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 ...
1answer
408 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 ...
1answer
371 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 ...
3answers
258 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? ...
1answer
188 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 ...
3answers
375 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 ...
1answer
127 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 ...
1answer
189 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, ...
1answer
255 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 ...
1answer
118 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 ...
1answer
331 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 ...
1answer
288 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: ...
1answer
254 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: ...
1answer
70 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 ...
3answers
254 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 ...
3answers
281 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 ...
2answers
167 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 ...
1answer
79 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. ...
2answers
234 views

### Why do I keep getting the same random numbers?

I am trying to use Mersenne Twister pseudo random number generators as seeds for my Monte Carlo simulations. So I tried ...
0answers
82 views

### Why OpenCLMersenneTwister[50] returns OpenCLLink::nodev: OpenCLLink failed to detect a usable device

I did the following: Needs["OpenCLLink`"] OpenCLMersenneTwister[50] (per documentation) on both my Dell Inspiron 530 Desktop PC (Radeon X1300/X1500 Series card) ...
2answers
265 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 ...
2answers
328 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 ...
3answers
615 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 ...
1answer
120 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. ...
1answer
150 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 ...
4answers
488 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 ...
4answers
430 views

### How to generate random directed connected graph?

How to generate random directed connected graph? I need to create graph which will pass: ConnectedGraphQ[^]
3answers
675 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 $0.7$.
5answers
440 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?
1answer
319 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 ...
1answer
305 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 ...
1answer
393 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 ...
2answers
1k 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 ...
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