# Tagged Questions

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

139 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 ...
213 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: ...
73 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 ...
531 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 ...
95 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 ...
96 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. ...
89 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. ...
120 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 ...
304 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 ...
53 views

I have data ...
65 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 ...
207 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 ...
598 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 ...
78 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: ...
577 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 ...
303 views

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

Bug fixed in version 10.2.0 My code is: ...
222 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 ...
105 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 ...
44 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 ...
142 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 ...
43 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 ...
77 views

### usage of random numbers in recursive loop

I am trying to evalute two functions using iterative process as below ...
376 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 ...
331 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 ...
80 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 ...
67 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 ...
436 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, ...
213 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 ...
170 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 ...
409 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 ...
97 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 ...
237 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 ...
168 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 ...
145 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 ...
51 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 $var(\epsilon_t)$ ...
93 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 ...
421 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 ...
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 ...
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: ...
50 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 ...
110 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 ...
99 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 ...
421 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 ...
84 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? ...
118 views

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105 views

### Sum considers RandomInteger[] as a constant

Perhaps this is expected behavior, but I was kind of surprised by the following: ...
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: ...
856 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 ...