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

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1answer
37 views

Variable Definitions and Random Numbers [closed]

I have currently created the following matrix: m={{RandomReal[{0,1}],RandomReal[{0,1}]},{RandomReal[{0,1}],RandomReal[{0,1}]}} In other words, a $2 \times 2$ ...
10
votes
2answers
166 views

Possible bug in VonMisesDistribution?

Bug introduced in 10.2 or earlier and fixed in 10.3 Observe: ...
1
vote
1answer
102 views

How to repeatly use random number generator in optimization problem

I am looking to run the optimization problem. I already finish my optimization code as below. ...
1
vote
0answers
54 views

Mixture of a bivariate distribution defined as a copula

I define a bivariate distribution: ...
4
votes
1answer
143 views
5
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3answers
124 views

ImplicitRegion gives arbitrary boundaries

This question uses Mathematica 10.2.0.0. equation1 is the major unbounded region I would like to generate: ...
3
votes
2answers
470 views

How do I generate n random numbers with an extra condition [duplicate]

I need to generate n random numbers that would sum into a. And I can't find an elegant solution here: https://reference.wolfram....
2
votes
3answers
537 views

For loop in Length computation code

Here is a code I wrote that is supposed to give the length of list after some splitting and regrouping. But it is inefficient. Is there a way to rewrite in more professional and efficient way? I guess ...
5
votes
2answers
160 views

How to find an estimated root efficiently with binary stochastic estimation of the function?

I am trying to construct certain nice geometric patterns, and one particular feature I'm trying to optimize is the balance of black and white corresponding to point being inside, or outside a ...
1
vote
3answers
363 views

Random non-overlapping disks in a square

I've found a nice code snippet by @belisarius from this question, that I'll reproduce here for reference: ...
2
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1answer
81 views

How do I define a random variable involving Part?

I need to define a random variable that involves Part, but when I try, for example ...
13
votes
1answer
595 views

What function generates random numbers in a compiled function?

I am writing a simulation for 2D random walk. I wrote several version of code, and found that the speed is like this (fastest to slowest): C++, Mathematica compiled procedural code, Mathematica ...
0
votes
0answers
140 views

Retrieving forthcoming step size from NDSolve

I'm solving a system of ODEs with a random component, which changes at each calculation step and depends on the step size. So I'm trying to realize something like this: (1) size of the forthcoming ...
6
votes
1answer
99 views

Slow-down encountered for RandomChoice in large lists

I was wondering if anyone could help me to speed up this code snippet which creates simple (sparse) networks by preferential attachment. The algorithm adds a vertex and an edge each time interval. ...
2
votes
2answers
100 views

Better to use loop or function when populated list?

In the past I have pretty much stuck to expression building when using Mathematica, but recently I have been writing a procedure to populate an array, which I guess are called "lists" in Mathematica. ...
1
vote
3answers
153 views

Partitioning List Into Sublists of Length 2 With The Pairing Being Random

I've done a bit of Googling with hopes of finding an answer, but to no avail. I'm looking for a way that I can have Mathematica take the elements of a list, say ...
3
votes
1answer
355 views

Plotting random circles in a square

How can we draw 20 circles which have random radius in a specified range, with random positions. All centers must be in a square with side=10 (for example centimeter): every overlapping between any ...
5
votes
1answer
82 views

RandomGraph with specific constraints

I need to generate random connected simple graphs (no loops) with the constraint that exactly two vertices must only have a single edge. I can create many connected graphs (but very few will have the ...
12
votes
1answer
229 views

Regime Change Stochastic Process

I would like to simulate an Ito process in which the drift and diffusion terms change after hitting a boundary for the first time. For example, a Geometric Brownian Motion X which has 0 drift and ...
5
votes
2answers
841 views

Simple Monte Carlo simulation

I want to find the Monte Carlo simulation of the integral $$\int_0^1 \sqrt{1-x^2}\mathrm dx$$ The Cesàro mean is $$I_n=\frac1n\sum_{k=1}^{n} f(U_k) $$ I want to plot the scatter plot ((1,$I_1$)(2,$...
1
vote
2answers
100 views

Calculating Variance (without Variance expression)

I am learning Mathematica on the fly, one of my tasks is to find the variance of white noise. I followed the tutorial for finding white noise by using the code: ...
11
votes
2answers
676 views

Generating uniform random points over a binary image

So I recently read this excellent post about generating random points over arbitrary regions. I hope Wolfram eventually builds that functionality into Mathematica's Random functions. I want to do this ...
8
votes
2answers
351 views

What's wrong with NIntegrate with “MonteCarlo” Method?

Bug fixed in version 10.2.0 My code is: ...
4
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3answers
308 views

How do I draw random points from a region [duplicate]

as the title,this problem have confused me a whole day.If I have a region,how can I yield a random member in this region.The region such as ...
2
votes
2answers
176 views

How do I execute a block of code multiple times? [closed]

Rudimentary pseudoconceptial question: I have a specific block of code that uses random variables and generates a plot at the end based on random code. I want my code to run 10 different times to get ...
0
votes
0answers
47 views

Parametrizing a matrix given its trace and norm

I have a problem where I have to generate random matrices with the following properties: ($a$ is a given fixed number) $\mathrm{Tr}\, A=0$ $\mathrm{Tr}(A^\dagger A)=\|A\|_F^2=a$ I was wondering ...
0
votes
2answers
169 views

Generate a list with random values between a and b [closed]

I am trying to perform system identification.. To properly identify the system i have to give the system a "rich" signal which are able to "activate" all the modes of the plant. A rich signal would ...
2
votes
0answers
50 views

Custom graph distribution

I am working with random graphs a lot. It's quite easy to describe random graph using, adjacency matrix or just a list of edges. However I am thinking that I might benefit from describing random ...
0
votes
1answer
92 views

usage of random numbers in recursive loop

I am trying to evalute two functions using iterative process as below ...
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} ...
22
votes
1answer
425 views

Generating animations of clouds with Mathematica

I'd like to generate some visually-pleasing animations of clouds, fog or smoke with Mathematica. My idea of "visually-pleasing" is along the lines of one of the images on the Wikipedia article for ...
1
vote
2answers
388 views

How to generate a random, relatively prime number to p?

I'm sorry if this is an obvious question, but I'm a newbie and googling didn't help me much. Is there a way in Mathematica to generate a number q coprime with <...
1
vote
3answers
84 views

Fill an array, symmetric with respect to its centre

I want to create an array that must be symmetric with respect to the centre of it, as in the following example: 0 1 2 3 4 3 2 1 but, instead of having such ...
0
votes
1answer
69 views

How do I apply a conditional append rule to plot randomly chosen points?

I'm working on an attempt at forming a sort of "Mandelbrot" set using Newton's method and randomly chosen points. Effectively I need to define a loop for Newton's method to determine whether my points ...
8
votes
3answers
473 views

Turning a set of random walk data 45 degrees

I have a set of data that is just a "random" (generated by me, not by computer) sequence of length 2000 of 1's and (-1)'s. I used it to plot a 1-D random walk where +1 is step up, (-1) is step down, ...
1
vote
1answer
250 views

Combining Mandelbrot and Monte Carlo

I'm trying to combine plotting a Mandelbrot set with Monte Carlo randomization to plot an equation using random points for complex number z, for the function $z^3-2z+2=0$. Below is the code I have ...
1
vote
2answers
376 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 ...
9
votes
3answers
454 views

Simulate random data with correlation

I would like to simulate some random data e.g. between 0 and 1, but with a given correlation. In other words some data where the correlation between two datasets is e.g. a constant or within a give ...
4
votes
0answers
118 views

RandomVariate, MSE and Cramer-Rao bound calculation

I'm using the following code to plot the variance of a moment estimate of a parameter of Rice distribution and its' Cramer-Rao bound. First I generate $10^3$ vectors $\texttt{R}$ ($10^3$ elements ...
0
votes
1answer
279 views

Random numbers in C++ and Mathematica gives wrong results? [closed]

I have the following strange phenomenon which puzzles me!: I have a piecewise constant probability density given as ...
3
votes
1answer
190 views

Failed to create a special random-disturbed initial condition for partial differential equation [closed]

I try to use BSplineFunction to creat a initial condition for NDSolve which has periodic boundary condition, that is realized by ...
0
votes
1answer
174 views

Generate a small random disturbance on a flat surface for NDSlove

I want to generate a small random perturbation on a flat surface defined on a square domain, e.g. 1 + 0.05 rand(x,y), which can be used as initial condition with periodic boundary conditions in ...
0
votes
2answers
59 views

Simulate from an AR(1) process where the parameters vary over time

I would like to simulate from an AR(1) process, where the $\rho$ parameter in the process of the form: $X_t = \rho X_{t-1} + \epsilon_t$ varies over time. The path of $\rho$ and $var(\epsilon_t)$ ...
0
votes
1answer
96 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
442 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
77 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
59 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 ...
2
votes
0answers
165 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
156 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 ...