Questions about random number generation and the properties of numbers so generated.
1
vote
0answers
52 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
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 $\frac{dx}{dt}=\eta(t)$
1
vote
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]
...
2
votes
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 ...
15
votes
1answer
454 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
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, ...
10
votes
1answer
175 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
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.
...
3
votes
2answers
140 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 ...
1
vote
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 ?
...
0
votes
1answer
130 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
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 :
...
-4
votes
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 ...
10
votes
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 ...
1
vote
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 ...
27
votes
5answers
986 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
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 ...
17
votes
1answer
287 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 ...
12
votes
1answer
412 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 ...
23
votes
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 ...
3
votes
3answers
261 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?
...
6
votes
1answer
189 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 ...
10
votes
3answers
376 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
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 ...
0
votes
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, ...
1
vote
1answer
256 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 ...
0
votes
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 ...
8
votes
1answer
333 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
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:
...
14
votes
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:
...
0
votes
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 ...
1
vote
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 ...
13
votes
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 ...
2
votes
2answers
168 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 ...
0
votes
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.
...
-10
votes
2answers
236 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
...
0
votes
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) ...
9
votes
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 ...
8
votes
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 ...
8
votes
3answers
617 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
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. ...
9
votes
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 ...
5
votes
4answers
489 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
432 views
How to generate random directed connected graph?
How to generate random directed connected graph?
I need to create graph which will pass:
ConnectedGraphQ[^]
6
votes
3answers
676 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 $0.7$.
4
votes
5answers
441 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?
11
votes
1answer
320 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
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 ...
1
vote
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 ...
25
votes
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 ...
