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

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0
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2answers
66 views

Getting RandomChoice to work in Manipulate function

I'm a beginner mathematica programmer and I am tryin to create my first demonstration. This code should represent what happens if one changes the size of the reading frame, calculating the nucleotide ...
2
votes
2answers
1k views

Generate nonoverlapping random circles [duplicate]

I want to distribute n circles unformly in an area(e.g. free plannar space). The circles could touch each other but cannot overlap. ...
0
votes
0answers
72 views

How to randomly create disks with randomized radii under given specific cover ratio? [duplicate]

I want to create uniformly distributed disks(dots) in a specific rectangular area. Suppose: the disk radii should be uniformly between $a$ and $b$ ($0<a<b$); there is no interaction between ...
1
vote
1answer
91 views

RandomVariate form a Specific Distribution with Restrictions

There are a lot of questions about generating random numbers form both uni-variate and bi-variate distributions. Mathematica has a lot of built in distributions for that purpose. However, I could not ...
4
votes
0answers
67 views

Help with Multivariate ProbabilityDistribution

I wish to obtain numbers from ...
4
votes
1answer
321 views

Monte Carlo Volume Calculation and Speed Up

I am trying to do a Monte Carlo area calculation for an irregular area defined by: $$0 \le x \le 1, 10 \le y \le 13, y \ge 12 \cos(x), y \ge 10 + x^3$$ I used the code with modifications (so I can ...
12
votes
2answers
300 views

Sampling a phase space uniformly for a given energy?

The energy for a 1D harmonic oscillator can be written: $$ E = \frac{1}{2 m} p^2 + \frac{m \omega^2}{2} x^2 $$ where x is position and p is the momentum. I would like to sample phase space $(x,p)$ ...
5
votes
2answers
395 views

TemporalData, RandomFunction, Loops: Extracting data from TemporalData sets?

I'm doing a finance project for my differential equations class to explore stochastic processes. I'm exploring IRA retirement funds. From the project write-up: Standing assumption: at time of ...
12
votes
6answers
869 views

Generating Random Real numbers with certain numbers not included

I'm writing a program that i need 1000 real number between -3 and 6. the code that I used for generating and saving them was l = RandomReal[{-3, 6}, 1000] But I ...
4
votes
2answers
130 views

Generate non-overlapping permutations

Let l be a list l = Flatten[Range[7] & /@ Range[12]]; (* 1,2,3,4,5,6,7,1,2,3,4,5,6,7,... *) The question is to ...
0
votes
2answers
105 views

A constraint to RandomReal for sum of numbers equal to arbitrary n

I want to generate some random numbers but respect a constraint. So I use RandomReal[{0,1},N,WorkingPrecision -> 2] I want to fix a constraint in order ...
28
votes
3answers
440 views

Assign a randomly generated list to variable

Bug introduced in 10.0.0 and fixed in 10.0.2 I don't know if this is a silly question, but it really baffles me. So please help me understand this behavior. ...
1
vote
1answer
215 views

How to figure out the seed I used to generate several random numbers given that I didn't used SeedRandom at first place?

After generating thousands of random numbers, I figured out that I didn't used SeedRandom to store the seed. Is there a way for me to know what seed was used to generate these numbers? Thanks in ...
1
vote
1answer
318 views

Generate random nxn matrix with all negative eigenvalues

I need to generate an nxn matrix with random entries, but I also need all of the eigenvalues to be negative (real or complex doesn't matter). I have: ...
0
votes
1answer
89 views

Why does RandomFunction return variable number of data points?

I am using the following code snippet to generate Compound Poisson process random numbers: ...
3
votes
3answers
347 views

Coloring random points in an annulus

I have found the following random generator to generate points in an annulus in stackoverflow on stackoverflow ...
8
votes
3answers
318 views

Random Integer Sequences

I want to construct a random square matrix in the following manner: a) Three states [0 | 1 | 2] are repeated ...
1
vote
2answers
97 views

Verify positive definiteness using random numbers

I wish to verify whether T'T - IdentityMatrix[2] is always positive definite for a certain choice of elements of T'T. ...
2
votes
1answer
73 views

Parallelization and evaluation of random number generation

Suppose I have the following functions: ...
5
votes
3answers
1k views

Generating random symmetric matrix

Suppose first that I want to generate a matrix whose elements are independent and identically distributed (i.i.d.) with distribution dist. This is easy: ...
3
votes
2answers
120 views

Sublists of Random Permutations

What is an efficient way to create a list of (psudo)randomly chosen permutations? I'm trying to create a list like below: ...
1
vote
1answer
100 views

FindProcessParameters for Fractional Brownian Motion Returns Error

I have the following data: ...
3
votes
1answer
100 views

What ProcessEstimator Options can I use with FractionalBrownianMotionProcess

I can generate an fBm process: ...
8
votes
1answer
604 views

Computing the Hurst exponent or fractal dimension of fractional Brownian motion

The Hurst exponent is related to the fractal dimension by noticing that the fractal dimension $D$ is equal to $2-H$, where $d$ is the intrinsic dimension and $H$ is the Hurst exponent, for 1-D ...
8
votes
1answer
477 views

Optimizing Monte Carlo simulation of a Pred-Prey model

My assignment and code As part of an assignment for one of my classes, I'm trying to run a "massive" Monte Carlo simulation in Parallel on the follow model: ...
34
votes
8answers
2k views

How to generate random points in a region?

The Mathematica 10 documentation was updated for FindInstance adding support for regions. In my use case, I'm trying to sample points in a set of disks: ...
6
votes
1answer
246 views

Simulation Sample Paths for Stochastic Approximation Algorithm

Let $X_t$ be IID random variables in $[0,1]$ and CDF $F(\cdot)$. Suppose there exists a variable $Y_t$ given by: $Y_1 = X_1$ and $Y_t = \phi(X_t, \overline{Y}_{t-1}), \forall t >1$, where ...
30
votes
5answers
3k views

2D random walk within a bounded area

I want to simulate a random walk on two dimension in a bounded area such as a square or circle. I am thinking of using If statement to define a boundary. Is there a ...
1
vote
3answers
174 views

Random reals according to conditions

I'd like to create a list of triplets $(x,y,z)$ which satisfy the following properties: $$0<x<1/2 \\ 0<y<1/2-x \\ -1<z<-2(x+y)$$ Basically I would like to uniformly generate random ...
1
vote
2answers
198 views

Simulation Beta Distribution

Suppose a function such as: $\phi^{\alpha} (x,y) = \left\{ \begin{array}{l l} \alpha x & \quad \text{if $x < y$}\\ x & \quad \text{if $x = y$}\\ \alpha x + (1 -\alpha) & ...
16
votes
1answer
646 views

Speed up adding Poisson noise to an image

I'm simulating some images corrupted with Poisson noise, but I'm encountering a few problems with performance. According to the documentation on ImageEffect, one ...
2
votes
3answers
313 views

Create a list of random reals

How can I create a list of random pairs $(x,y)$ where $0<y<x<1$ and $x,y \in \mathbb{R}$ ? I can't seem to place that inequality restriction on the random numbers that are generated.
0
votes
0answers
32 views

Generating a Table with a certian Density [duplicate]

How do I create a random table of 0's and 1's with a certain density instead of a probability? For Example: Manipulate[ Table[RandomChoice[{1 - density, density} -> {0, 1}, {10}]], ...
0
votes
1answer
143 views

Simulated Annealing for NMinimize[] always returning the same solution

I have a function defined as follows: ...
6
votes
5answers
2k views

Random numbers that sum up to specific value

I would like to generate a list with random numbers, which add up to a specific value. While[Total[x] == 28, x = RandomInteger[{0, 28}, 5];Print[x]] The random ...
0
votes
1answer
206 views

Generate Random 3D Network using GraphPlot3D and loop

Instead of writing all this out I want to do the same thing with a loop and be able to manipulate n and k. The idea is to create a randomly generated network where n is the number of nodes and k is ...
1
vote
1answer
144 views

Probability Distribution of a Multivariate Hypergeometric distribution and maximum probability

Hello to all Mathematica Users! I have this question: Consider a box which contains 69 balls. 17 red, 1 white, 29 blue and 22 green balls. There will be picked 7 balls randomly, without putting the ...
4
votes
3answers
148 views

Creating nested matrix using random integers

How do i create 15x2 matrix with 2x2 random integer elements? My code only returned identical 2x2 elements:
3
votes
1answer
247 views

How to generate a random binary tree with a given number of vertices and with a given shape, namely compact or elongated

I tried to generate a random binary tree with a Table of RandomInteger and to give a shape with a ...
4
votes
4answers
620 views

Skip other If conditions

I'm trying to write a code to "random" move in a matrix but it can't go to a certain position if it has a certain value (in this case I'm using the number 2). How do I make it to skip all other If ...
4
votes
1answer
289 views

Simulating a bounded continuous random walk in $n$-dimensions

You're given three $n$-dimensional real vectors, $\mathbf{x_0}$, $\mathbf{a}$ and $\mathbf{b}$, with $\mathbf{a} \le \mathbf{x_0} \le \mathbf{b}$ (vector inequality means component-wise inequality). ...
3
votes
1answer
316 views

Plot A Function Of A Stochastic Process

I am trying to do something very simple in Mathematica 9. I want to play around with option pricing and for that I thought it best to use the new stochastic process functionality. So, first of all I ...
1
vote
1answer
202 views

How to generate a random signal consisting of the specified functions

Let's assume that I have some particular signal on the finite time interval which is described by function $f(t)$. It could be, for instance, a rectangular pulse with amplitude $a$ and period T; gaus ...
1
vote
1answer
166 views

Matrix and random, weighted assignment of rows

I asked a question in this category previously but my problem has changed. On one hand, I have a large number of data files as .dat format, and on the other hand, I have a matrix ...
2
votes
2answers
222 views

Generating $n$ random samples every time

Is it possible to generate $n$ random samples, and always ensure that $n$ samples are generated? eg For $n=5$: ...
3
votes
4answers
411 views

random split a dataset

I've got a very simple problem, but not so trivial. I need to split a dataset (input and output data) in three part randomly: training set 70%, validation set 20% and is test set 10%. First of all ...
1
vote
1answer
57 views

Replicability of RandomVariate within a function?

I have a rather basic question but can't figure out a foolproof answer. In the following code, I build a function which returns the mean difference between successive elements of a vector created from ...
0
votes
0answers
34 views

Table of values for functions with random variables [duplicate]

I'm trying to get a table of values for functions with random variables. First of all, i have a function like that: ...
6
votes
2answers
842 views

Distribution of 10 points within a unit square

Related to some packing problems, following problem arose: Distribute 10 points within a square of sides 1, so that minimal distance between them is maximized. With the help of random simulation, or ...
0
votes
1answer
249 views

Importing a text file into a matrix format

I am attempting to perform a comparison of pseudorandom number generation with the RAND Corporation's "A Million Random Digits with 100,000 Normal Deviates" for a Computational Physics course. I have ...