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

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4
votes
2answers
201 views

Calculate $\pi$ using Monte Carlo methods

I know that we can have an estimate of $\pi$ using Monte Carlo methods. I know that we make a huge loop and each time we take randomly two numbers in the range [0,1] and calculate the number of ...
0
votes
2answers
59 views

Random 3D cylinders plot [duplicate]

I have seen this trivial example for circles ...
2
votes
0answers
43 views

The correct assignment of probability distribution to generate random variables

I'm asking you for a help to solve a difficult (for myself) task. Now I will tell you what and why I'm trying to implement. The task is to simulate the passage of elementary particles through a ...
1
vote
0answers
41 views

Generating random Kraus operators

I am trying to generate (randomly) set of square matrices $\{K_m\}$ with the properties that $$\sum_{i=1}K_i^{\dagger}.K_i=I_n,$$ where $I_n$ is the identity matrix of order $n$. So, the input should ...
0
votes
1answer
50 views

Simulating a Boolean model in a uniform square

I am looking to simulate a Boolean model with specified Poisson point process. ...
0
votes
1answer
63 views

How to generate samples from an arbitrary continuous pdf?

If I define an arbitrary pdf p[x_] for a arbitrary-dimensional continuous variable x, how can I use Mathematica to create a function that will return a set of n random samples of x with distribution ...
2
votes
0answers
86 views

Optimization of custom probability distibutions?

Consider the two tests: Timing[Do[RandomVariate[NormalDistribution[0.5, 0.3]], {200}]] {0.001188, Null} ...
-1
votes
1answer
125 views

Periodic boundary conditions for two walkers

For some reason I'm getting infinite loops most of the time i run this. Perhaps the periodic boundary conditions are wrong. Seems like the probability of the two positions to be the same is extremely ...
-1
votes
1answer
80 views

Draw independent samples from conditional distribution at a fast rate

I would like to draw samples from the following conditional distribution of the following (don't ask why): ...
12
votes
2answers
296 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 $(x,p)$ ...
0
votes
0answers
3 views

Complexity of a randomly-traveled N*M grid [migrated]

I made an algorithm that compute a random-path across a N*M grid using backtracking. It start at [N / 2][0] and shall finish at [N / 2][M - 1]. Each iteration he choose a random direction (Left, ...
4
votes
2answers
563 views

Manipulate 2D random walk

Consider the first $10000$ digits of $\sqrt{2}$ and present them as a “random walk” by converting them in base 4 representing 4 directions. Following code produces this random walk ...
3
votes
3answers
88 views

How to change random values in manipulate?

I made a Manipulate box that is working very well, using lots of random numbers. I would like to add a button to "reset" (i.e. to change, randomize, or reselect) all the random parameters. Here's ...
1
vote
2answers
85 views

Animated discrete plot for a generalised random walk

I have a number of possible outcomes $R=\{r_i\}$, with $r_i\in\mathbb{Z}$ and corresponding probabilities of occurrence $P=\{p_i \}$, with $p_i \in [0,1]$ and $\sum_i p_i=1$. I am wondering whether ...
3
votes
5answers
177 views

How to define a set of two random orthogonal unit vectors?

I need to define a random set of two orthogonal unit vectors. The code below doesn't give proper unit and orthogonal vectors : ...
1
vote
1answer
74 views

How to define a stochastic electromagnetic field? [closed]

I would like to show the effect of a stochastic electromagnetic field on a relativistic charged particle, using a manipulate box. The field should be randomly varying in time and in space, and be ...
0
votes
0answers
69 views

Maximum Likelihood Estimation of Gamma-distribution Scale parameter

I have the following tasks: Generate random sample with given parameters shape = 2, scale = 0.001 and shape = 2, scale = 1/1200 for the right censored sample; Using Maximum Likelihood Method ...
3
votes
0answers
28 views

Missing Completely at Random MCAR

Many other stats packages have tests for MCAR but Mathematica doesn't seem to. Have a I missed something? If not what would a simple implementation in MMA look like. (disclaimer I'm new to MCAR ...
3
votes
3answers
87 views

Random bipartite graphs?

RandomGraph[{n,m}] generates a random graph with $n$ vertices and $m$ edges. I want to generate a random bipartite graph, like ...
1
vote
2answers
124 views
18
votes
1answer
290 views

What pseudo-random number generators are available to Mathematica users?

One would think I should be able answer the question I pose in the title for myself by reading the Documentation Center article ref/SeedRandom, but it's not so simple. That article does give a list ...
13
votes
2answers
456 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 ...
1
vote
1answer
144 views

Bounded random walk

I have a random walk algorithm that I want to implement, but I am getting a recursion depth issue. I am making a list of points that Z particles can be in over the ...
4
votes
2answers
380 views

Colors associated to parts of a 3D distribution of points

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

Drawing a 3D Poisson Point Process with intensity $\lambda$

Can anyone suggest me a way of drawing a 3-dimensional Poisson Point Process (PPP) with intensity $\lambda$ in Mathematica. The points are located only in a half sphere. The 3-dimensional ball of ...
5
votes
2answers
88 views

Convergence data for Monte Carlo NIntegrate

I am using NIntegrate with Method -> "MonteCarlo" to evaluate a high dimensional integral. Is there a way I can obtain a list ...
10
votes
6answers
591 views

How do I randomly divide individuals into groups?

I would like to assign 'x' individuals to 'y' groups, randomly. For example, I would like to divide 50 individuals into 100 groups randomly. Of course, with more groups than individuals many of the ...
8
votes
2answers
506 views

Monte Carlo integration with random numbers generated from a Gaussian distribution

I want to do numerical integration of some functions using the Monte Carlo method. The default setting for the Monte Carlo method is to use a uniform distribution as far as I know. How can I change ...
6
votes
3answers
260 views

How can I create a random symmetric matrix in this way?

The most straight forward way for me to think about is like this: ...
4
votes
6answers
903 views

Randomly Multiply OR Divide by a Random Number?

I want that Mathematica decides randomly if a given variable, gets multiplied or divided by a random number in a given range. The "naive" idea to just use ...
1
vote
1answer
74 views

Random phases at each run in a wave superposition [closed]

I need to define a function which generates a random real number between 0 and $2\pi$, as a random phase constant for a wave superposition. The output should be different each time I re-run the code, ...
0
votes
2answers
60 views

generate “dynamic” random variables?

I have the following problem: I generated two random numbers ...
5
votes
2answers
221 views

How to generate a random pulsar graph between two points?

I am going crazy trying to create this. I am trying to create a pulsar graph that starts and ends on two points that have the same y smoothly along the x axis. The pulsar should have random valleys ...
4
votes
1answer
129 views

Find random $n$ combinations of values with a given sum

This problem is described in the related StackOverflow question: Find all combinations of coins when given some dollar value. I would like generate a list of $n$ combinations of values that sum up to ...
7
votes
4answers
230 views

How to generate two group of $n$ random numbers in $U(0,1)$ such that sum of these two groups equal? [closed]

I want to have two groups of $n$ random numbers $u_i$ and $v_i$ in $U(0,1)$, such that $\sum u_i = \sum v_i$ What I tried is: I can firstly get $u_i$ by ...
3
votes
1answer
137 views

Random Variate generating strange results when using ProbabilityDistribution

I have created a probability distribution that follows a general normal distribution, given by: $$ \frac{b *e^{-\left(\frac{\sqrt{(x-u )^2}}{a }\right)^{b }}}{2 a \Gamma \left(\frac{1}{b }\right)} ...
6
votes
0answers
77 views

RandomPoint works with a 2D ImplicitRegion but fails for any higher dimension

This is inspired by this answer which features code that I cannot get to work at all, and I tried to figure out why. It boils down to using the function ...
7
votes
1answer
148 views

Why is Random faster than RandomReal?

As of version 6, Random[] was superseded by RandomReal[ ] etc, but both still work perfectly well. Playing with some timing ...
7
votes
1answer
78 views

RandomPoint fails with a large enough number of points

Bug introduced in 10.2.0 and fixed in 10.3.1. RandomPoint is new in 10.2.0. I have defined a simple ellipsoidal parametric region: ...
3
votes
3answers
151 views

Smooth initial data

I need something that produce pseudorandom smooth initial data for modelling phase separation equations (Cahn-Hilliard and simular). Generator code for now: ...
1
vote
1answer
49 views

Generate a simulated covariance matrix

I am working on a problem where one of the input variables is the level of covariance between the entries in a particular matrix. To simulate this problem in Mathematica, I will need to feed my code ...
1
vote
2answers
143 views

Handling of Temporal Data [closed]

I use a random function of a process which yields a Temporal Data object, I need but do not know how to recuperate the numerical values of the process in a Table from the Temporal Data.
4
votes
2answers
140 views

Confining/Periodic boundary conditions implementation for 2D Random Walker

I am new to Mathematica, and am having trouble implementing confining boundary conditions for a random walk simulation confining the walker to a pre-defined region (periodic boundary conditions would ...
1
vote
1answer
216 views

What is the fastest way to obtain the eigenvalues of a Wishart matrix?

I would like a fast method of creating a sample of random numbers which corresponds to the eigenvalues of a Wishart matrix: For M>N the eigenvalues \lambda_i are given by the jpd Where $K_N$ is ...
1
vote
0answers
82 views

Manipulate a random walk [closed]

For a college project I am manipulating a random walk. I managed to make a walk but in the manipulation every time a step is added the manipulation shows an entirely different walk. I understand why ...
1
vote
2answers
325 views

Finding uniformly distributed random points on an ellipsoid

I am trying to generate a poincare map for a system whose reduced energy manifold looks like the following surface. (x/a)^2 +(y/b)^2 +(z/c)^2=1 I want to find a ...
1
vote
1answer
102 views

How to use a random number generator as an independent variable in an existing model?

I am relatively new to Mathematica and I need some help regarding how to create a random number generator to be used as an independent variable for a model my group has been working on. Following is ...
5
votes
1answer
125 views

How to make my fuction return a step count

I am new to mathematica, and I have this 3d random walker program which runs with a fixed (given) amount of steps. What I want it to do is to run forever but stop when two walkers collide (aka have ...