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

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0
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1answer
94 views

How to improve this function that selects parameters from arbitrary distribution using Recursion?

Below, I have defined a function using Which to select model parameters based upon various conditions. My questions are: Is there any danger in writing this function using Recursion? Is there a more ...
10
votes
5answers
427 views

How to randomly select subsets

I have a list of around 300 elements. I want to sample subsets of length 25 such that my samples are all distinct. My first inclination was to use something like ...
16
votes
3answers
2k views

Can Mathematica's random number generation be improved?

Performance on Random Number generation is intolerable. Whenever you need many deviates from the same distribution but with different parameters it takes forever. Here is a thread on Poisson ...
2
votes
1answer
63 views

Why is RandomVariate of special probability distribution doesn't working in all cases

I would like to generate a random variates in Mathematica 9 with this distribution: ...
0
votes
1answer
54 views

Fit process parameters to a transformed AR(1) process

I would like to fit the parameters of an exponented AR(1) process using Mathematica's EstimatedProcess, however, the function does not seem to evaluate to anything. First of all I create the ...
1
vote
0answers
127 views

Von Neumann's method to generate points uniformly distributed on a region of a n-sphere surface

I am trying to generate points uniformly distributed on a region of a single n-sphere surface (all angles in hyperspheric coordinates are between 0 and Pi/2). I decided to use von Neumann's method ...
2
votes
1answer
123 views

Time inhomogeneous Markov Chain in Mathematica

I would like to create a discrete 2-state Markov process, where the switching probabilities in the transition matrix vary with time. I can currently do the following, which creates a process with ...
4
votes
4answers
444 views

Creating a fast random array generator

I want to create N x N array of random numbers. (N is an integer). The constraints are, each element should be between 0 to l(integer) ( here 0<= l <= N) and the sum of elements in each row ...
0
votes
0answers
108 views

Random generation of three-non-collinear and four-non-coplanar points in 3D space

Please, take a look to this code. How it can be improved so that the time execution becomes smaller? ...
1
vote
1answer
128 views
6
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2answers
107 views

Sum considers RandomInteger[] as a constant

Perhaps this is expected behavior, but I was kind of surprised by the following: ...
26
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3answers
2k views

Generating 250 random points crashes the kernel, but not 249

Fixed in 10.1.0. Consider the following function, which generates uniformly random points on the surface of the 2-sphere: ...
3
votes
4answers
977 views

Random real numbers that sum up to specific value [duplicate]

In here, it works with "Integer". What if I want 5 positive real numbers that sum to 1? RandomChoice[IntegerPartitions[100, {5}]]/100. That will work. But only ...
0
votes
2answers
61 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
809 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
70 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
87 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 ...
3
votes
0answers
62 views

Help with Multivariate ProbabilityDistribution

I wish to obtain numbers from ...
4
votes
1answer
297 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
266 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
327 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
846 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
124 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
100 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
432 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
182 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
271 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
82 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
335 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
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3answers
316 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
96 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
68 views

Parallelization and evaluation of random number generation

Suppose I have the following functions: ...
5
votes
3answers
941 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
115 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
95 views

FindProcessParameters for Fractional Brownian Motion Returns Error

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

What ProcessEstimator Options can I use with FractionalBrownianMotionProcess

I can generate an fBm process: ...
7
votes
1answer
540 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
450 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: ...
32
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
240 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 ...
27
votes
5answers
2k 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
163 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
189 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
586 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
305 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
135 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
194 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 ...
0
votes
1answer
128 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 ...