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

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21
votes
5answers
1k 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
109 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 ...
12
votes
1answer
221 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 ...
21
votes
3answers
545 views

Which Distributions can be Compiled using RandomVariate

Recently, Oleksandr kindly showed a list of Mathematica commands that can be compiled. RandomVariate was part of that list. However, whether this can be compiled depends upon the distribution that is ...
15
votes
4answers
895 views

Finding the volume of a sphere using the Monte Carlo algorithm

I used the following code to find the volume of the sphere $x^2+y^2+z^2 = 1$ in the first octant: ...
0
votes
0answers
43 views

Random reals according to probability distribution [duplicate]

How do I generate a list a random real numbers that follow a probability distribution? If my pdf is $f(x)$, how do I "force" the random numbers to follow $f(x)$?
2
votes
3answers
265 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
30 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
77 views
4
votes
4answers
970 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 ...
6
votes
2answers
602 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
51 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 ...
3
votes
2answers
185 views

Addition of Matrices [closed]

How can I add the Matrices created by this: SeedRandom@0; Table[RandomInteger[{0, 34}, {2, 2}], {2}, {5}] // MatrixForm $\left( \begin{array}{ccccc} \left( ...
3
votes
3answers
112 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
127 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). ...
4
votes
4answers
556 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 ...
0
votes
1answer
75 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
69 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
116 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 ...
1
vote
4answers
177 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 ...
0
votes
2answers
183 views

Generating a random tree of given cardinality, depth, and labeling

For demo, exploration and teaching purposes, I would like to be able (and asking you for help) to generate these special instances of trees: For given: N - number of nodes in the tree D - depth of ...
2
votes
2answers
119 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 $n=5$: ...
1
vote
1answer
45 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 ...
8
votes
2answers
685 views

How could I generate words starting with P,h,D?

A friend of mine is a PhD candidate and posted a picture on Facebook with funny words starting with 'p', 'h' and 'd' like "Please hire. Desperate" or "Permanent head Damage". I thought I could try and ...
0
votes
0answers
29 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: ...
0
votes
1answer
58 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 ...
1
vote
3answers
137 views

How do I select only those lists whose elements are all above a certain number?

I'm essentially doing coin flips, using RandomReal to populate a bunch of lists, each with 8 elements. I then want to select only those lists for which all elements are greater than a certain number, ...
14
votes
3answers
600 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 ...
2
votes
2answers
160 views

Expectation of a family of random variables

I did some search here, but seems that no one asked about this. I want to define a family of independent and identically distributed random variables, $x_1,...,x_n$, and then calculates the expected ...
3
votes
1answer
55 views

RandomVariate does not evaluate a Hyperbolic Distribution

Any Idea why I can't get a result from this expression: ...
3
votes
5answers
167 views

Randomly selecting and reinserting a subset of elements in a list

This question is similar to my other question: How do I randomly select 'k' positions in a list and shuffle their respective elements without effecting the other elements? Imagine first a ...
0
votes
1answer
76 views

How to efficiently distinguish the rewired edges in WattsStrogatzGraphDistribution?

The WattsStrogatzGraphDistribution function is a way to construct random graphs based on Watts and Strogatz small world model. The ...
4
votes
1answer
131 views

How do I randomly select 'k' positions in a list and shuffle their respective elements without effecting the other elements?

Imagine I have some list: listA = {"a","b","c","d","e","f","g","h","i","j"}; I'd like to randomly select k positions in the ...
1
vote
1answer
88 views

Generating a random sample of elements from a list that includes a subset of the list

Imagine I have a list: tList = {item1,item2,item3,item4,item5,item6,...}, and I'd like to take a random sample of numItems ...
1
vote
0answers
75 views

How do I keep a random value associated with a locator point as points are added?

I have a Manipulate to which I am adding and removing Locator points (one of which is different from the others, though that is ...
5
votes
3answers
348 views

Fast code to generate large random graph with fixed degree sequence

I'm trying to create a function so to generate large random graph with a fixed degree sequence $\{v_1,v_2,\dots,v_N\}$, where $N$ is the number of vertices in the graph. The Mathematica function that ...
3
votes
1answer
177 views

Put random points into a specific 2D subregion

I want to cover a particular subregion of the x-y plane with a random distribution. As this particular region is not a circle I encounter some problems declaring the permitted zone where to put ...
1
vote
1answer
115 views

How to replace a list with the result list after each iteration [closed]

I have some initial values such as L1 list: L1={10,20,30,40,50}; I want to use the L1 ...
0
votes
1answer
85 views

Index of iteration inside NestList [duplicate]

I have a list of RandomReal: delta = RandomReal[{-0.01, 0.01}, 1000] I want to add each element of the list to the ...
6
votes
1answer
192 views

Generating a (random) 2-dimensional cellular network

I want to generate a network of random cells like the following picture: The general idea is to generate some random points (x,y) as coordinate of a vertex and then randomly choose some of these ...
1
vote
3answers
175 views

How to update a list in a function in each iteration

There is a list with numbers 1 to 8 ( p1 ) and another list (j) which contains 4 numbers which shows different 4 positions of ...
1
vote
0answers
103 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 ...
1
vote
3answers
179 views

How to replace identical positions in two different lists

Assume that I have two lists like : list1={1,2,3,4,5}; list2={a,b,c,d,e}; I want to replace some elements from list1 into ...
14
votes
5answers
798 views

Picking random items out of a list only once

I'm trying to create a function that randomly returns a value from a list but remembers the values that have been given before. At the end when the list is empty it should return an empty list. ...
0
votes
1answer
50 views

How to put some values from a list into a function in a Do loop

I want to program a code in MATHEMATICA in order to calculate some values in different iteration. For example, assume this list: list={1,2,3,4,5} Now assume that ...
1
vote
2answers
77 views

Avoid making repeated Random Integer in different iterations

Assume following code : Do[ i1 = RandomInteger[{1, 5}]; i2 = RandomInteger[{1, 5}]; While[i1 == i2, i2 = RandomInteger[{1, 5}]] , {k, 1, 4}];` This ...
14
votes
1answer
305 views

Making Monte Carlo simulation with ParallelTable

I would like to to MonteCarlo simulations of various regressions - basically, doing OLS under various conditions to test approaches. On my macpro 2x 2.8 GHz quad core Xeon, 32 Gb RAM DDR2 @ 667 Mhz, ...
0
votes
2answers
80 views

Multiplying a list and randomly re-assigning that list to a series of numbers

I'm trying to write a script that matches a particular element to a coordinate. Let's say there are 24 coordinates; and that fractionally a:b:c:d:e is 18%:18%:18%:18%:27%. Instead of matching 4 of a, ...
2
votes
3answers
118 views

Performance on Multinomial Deviate is slow

Most of the time in my program is spent on this single line of code: out = RandomVariate[MultinomialDistribution[nt, tmp]]; ...
8
votes
1answer
152 views

Inconsistent DistributionFitTest results?

In pondering this question, I used Mariana's function to generate the following data. ...