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

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8
votes
1answer
170 views

Gillespie Stochastic Simulation Algorithm

The Gillespie SSA is a Monte Carlo stochastic simulation algorithm to find the trajectory a dynamic system described by a reaction (or interaction) network, e.g. chemical reactions or ecological ...
11
votes
2answers
3k views

What is the best distribution for my histogram?

I defined a security bound for a random walk (cube with 15 length) and I have this code to obtain a sample of the random times at which the random walk crosses the boundary for the first time: ...
10
votes
3answers
1k views

Random walk on a sphere

I'm trying to program a random walk on a sphere with Mathematica. I found this code while I was searching, but I'm not getting results from it. I waited an entire day, but my PC didn't finish ...
0
votes
2answers
80 views

How do I save the generated 2d random array for the next use? [duplicate]

I generated a 2d random array in $x-y$ plane with L = 10; random = Table[{x, y, RandomReal[{-1, 1}]}, {x, 0, L, L/10}, {y, 0, L, L/10}]; Now I want to save it ...
7
votes
1answer
94 views
9
votes
1answer
217 views

Random walk on a Sierpinski gasket

I am trying to simulate a random walk on a Sierpinski gasket. The best strategy i could come up with is to use Nearest point function to determine the next possible step of my walker. But this creates ...
1
vote
2answers
83 views

Selecting and plotting points belonging to a region from a random sample

I'm facing a problem with RandomReal when using ListPlot to plot some constrained points. I found that at every run of MA kernel ...
7
votes
6answers
2k views

Vectors with a certain magnitude in Mathematica

For a user-specified magnitude, is there a way to have Mathematica produce any 3D vector with that magnitude?
3
votes
5answers
254 views

Generating a two-dimensional random walk [closed]

I am new to programming inMathematica, and I am trying to pick up a few things by myself. As an exercise, I wanted to generate a two-dimensional random walk starting at the origin, and then moving a ...
11
votes
2answers
264 views

Efficiently generating samples from an urn with maximum per element constraint?

I need to sample from a distribution that is a hybrid of uniform and hypergeometric in the sense that all elements are sampled uniformly until an element reaches some specified maximum observations, ...
2
votes
0answers
61 views

How to use Compile? Bivariate Gibbs Sampler

I am trying to use compile to speed up my Gibbs sampler. I know I can use Reap and Sow to speed up tremendously. I have a more complicated Bayesian posterior that I want to speed up with compile so I ...
1
vote
1answer
67 views

Classifier Random Forest Accuracy Not Consistent

I tried running a random forest classifier over different training sample sizes. The results are very strange because I could not replicate my accuracy with the same sample size in the second ...
4
votes
2answers
268 views

Calculating overlapped area between random circles

Suppose I am plotting random circles like in the following example: m=125; ...
2
votes
2answers
115 views

Generation of six Random numbers related by a constraint

I want to generate six Random numbers $a,b,c,d,e,f$ (all are real and positive). They are related by $a^2+b^2+c^2+d^2+e^2=1$ and $f$ is between 0 and 3. How can I generate those numbers?
2
votes
2answers
49 views

Randomized Control of Time Series Data

I am trying to randomize the order of a time series data set. I generated my data as: ts5 = RandomFunction[FractionalBrownianMotionProcess[.5], {0, 999, 1}] ...
6
votes
3answers
237 views

Creating a custom distribution with specified skew and kurtosis

Let's say I want to create a simulated sample of returns for a given investing/trading strategy. I know that my strategy is profitable on 64% of trades, that the ratio of mean win / mean loss is 0.72, ...
2
votes
1answer
81 views
3
votes
2answers
275 views

Generate a random PDF

How can I generate a random probability density function $p(x)$ in the domain $[0,1]$? Is there a single Mathematica function to do so?
10
votes
1answer
140 views

RandomInteger: speed with long lists

I noticed an interesting effect with RandomInteger when looking at the time to create 10^8 random integers. The following code lines all take about 0.5 seconds on a ...
4
votes
2answers
253 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
76 views

Random 3D cylinders plot [duplicate]

I have seen this trivial example for circles ...
2
votes
0answers
74 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
46 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 ...
1
vote
1answer
53 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
70 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 p?...
2
votes
0answers
89 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
127 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
84 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
302 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 $(x,p)$ ...
4
votes
2answers
573 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
94 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
94 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
198 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
79 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
80 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
29 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
106 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
166 views
18
votes
1answer
298 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
479 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 non-...
1
vote
1answer
153 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
383 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
97 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
99 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
624 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
581 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 ...