# Tagged Questions

A vast area which includes generating results from computer models.

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### How to generate integer random numbers that equal to another random number?

I am running a simulation in Excel, and need to generate a group of integer random numbers summing up to another random integer, how can I possibly do it? For instance I have an integer random number ...
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### Time between arrivals Distribution

I am simulating a hair parlor queue with m number of queues and 3 different types of services (queues). I was doing the time between arrival with a uniform distribution with a min value and a max ...
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### Simulating r.v.'s from a joint density by rejection sampling in R. Continued

I wish to sample variables $v$ and $w$ from the joint density $$(v+w)e^{-\frac{(v+w)^{2}}{2x_{0}}-2\mu v-(\mu -\lambda )w},$$ where $x_0$, $\mu$ and $\lambda$ can be seen as positive constant. Since ...
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### Finding density and distribution functions [closed]

I have been trying to understand probability by attempting past paper question and I have been stuck on this question all day and night. I am not quite sure how to go about finding the functions ...
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### Stability of boostrap confidence intervals

As a word of background, I want to show that certain result is stable when averaging over a large number of simulations, but could be just a lucky draw with a small number of simulations. I have a ...
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### Simulating r.v.'s from a joint density by using rejection sampling in R

I wish to sample variables $v$ and $w$ from the joint density $$(v+w)e^{-\frac{(v+w)^{2}}{2x_{0}}-2\mu v-(\mu -\lambda )w},$$ where $x_0$, $\mu$ and $\lambda$ can be seen as positive constant. Since ...
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### Personal Experiences with Probability Simulation

Simulations methods are increasingly used in theoretical and (especially) applied probability. Personally, I have used simulation for purposes that range from recreational Q&A to applications of ...
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### exponential distribution with probability about texts

It is 9:00 p.m. The time until Joe receives his next text message has an exponential distribution with mean 5 minutes. A text has not arrived for 5 minutes. Find the probability that none will arrive ...
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### Sinusoid with zero boundary conditions on $[0,1] \times [0,1]$ grid

I want to make a sinusoidal plot (any shape is welcome) on a $[0,1] \times [0,1]$ grid, with boundary conditions equal to zero. It should resemble a membrane fixed along its edge. I tried out some ...
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### Evaluating Difficult Monte Carlo Integration in R

I recently posted a simple version here (Simple Monte Carlo Integration). I was able to verify that the answer was indeed close to 1/3 when I wrote the following R code, and got a mean of X of ~1/3: ...
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### Difference and confidence intervals

I performed a few series of simulation to evaluate values of two parameters. Let's say, the results can be presented like this: ...
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### Is Principal Component Analysis applicable to this type of situation?

I'm trying to model the response of ant populations to pheromones in this way: The ants are simulated as Self Propelled Particles with internal energy. They undergo acceleration due to their internal ...
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### Is it possible to estimate $e$ based on $N$?

Consider a sequence of random numbers $u_1,\dots,u_n$ obtained from a continuous distribution $F$. Let $N$ be the first one that is greater than its immediate predecessor. In othe words, N=\min_n\{...
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### Simulate correlated $\chi^2$ distribution

I understand that when one have multiple independent variable that follows $N\sim(0,1)$, denoted as $A$ if we have a correlation matrix $R$, we can generate correlated variables $B$ that are normally ...
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### mean and std deviation from little's law

I have a service node with a queue The arrival rate in this service node is exponential(0.4) The service time is exponential(0.2) Running a simulation i've calculated the average population of the ...
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### Monte Carlo sampling and Kolmogorovâ€“Smirnov test in practice

I have two deterministic algorithms, Algorithm 1 and Algorithm 2. The first has $m$ inputs and one output, and the second has $n$ inputs and one output. The distributions of the inputs of the ...
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### Statistics Marble Simulation

Given the jar containing 20 red, 5 white, and 10 blue marbles, Joey thinks a more interesting problem would be to find the number of marbles you would have to draw, without replacing them in the jar, ...
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### Can you simulate from a cantor distribution?

Has someone run across a method for generating random variates from a Cantor Distribution? It seems like its abstract definition prevents this. In essence, can one "invert" the Cantor Function?
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### How to efficiently simulate successes of several trials if probabilities are inhomogeneous

If I'm doing a simulation with $n$ trials, each with probability $p$, a quick way to select the successful trials is to choose a binomially distributed random number. Then randomly choose that many ...
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### What platform is best for simulating a stochastic process on a graph/network?

I'm simulating a dynamic process which was so far done only on a lattice, and Matlab was quite sufficient for that. However, I can't seem to find a convenient way to model such a process on a graph ...
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### Permutation algorithm for simulating random variables $X,Y,Z \in [0,1]: X+Y+Z = 1$ and $X,Y,Z \sim U(0,1)$

Edit: Sorry, I tend to jump back and forth between math notation and computer science notation....often to the chagrin of my more rigorous colleagues (and Math.SE folks ;-) Also, I accidentally ...
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### Looking for Method to evaluate the optimal node rate vs number of simulation rate in a Monte Carlo simulation

I am currently working on evaluating an American Option using a Monte Carlo simulation, and I am getting answers but they vary quite a bit. The two variables that I can alter are number of simulations ...
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### uniqueness of svd decomposition and its role in statistical analysis

let us consider following model according to following link http://www4.ncsu.edu/~ipsen/REU09/chapter4.pdf it says that : The singular values are unique, but the singular vector matrices are ...
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### Probability that winner of tournament is best player

There are $2^n$ players with skills $1, 2, \ldots, 2^n$ where the probability of Player A winning any game (against B) is $\text{skill}(A)/(\text{skill}(A)+\text{skill}(B))$. Set up a tournament of $n$...
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### Simulating elastic collision

I wrote a simple program where i can move around some objects. Every object has a bounding box and I use hooke's law to apply forces to the colliding objects. On every tick, I calculate the forces, ...
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### Tissue Deformation Simulation using FEM

I need to simulate tissue deformation using FEM. Is it advisable to represent the object as a triangle mesh or a ...