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0
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1answer
13 views

Coarse grid vs. Fine Grid [on hold]

I have a question regarding numerical simulations. Does anyone know what is Coarse grid and what is fine grid? With Thanks
0
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0answers
14 views

Expected Probability of a Random Agent and a Probabilistic Agent

I'm running simulations on two agents: random agent and probabilistic agent. The world they are running in is the Wumpus World where the agent is dropped in a 4x4 grid where each cell has a 20% chance ...
2
votes
0answers
10 views

orderstatistics of uniform distributions on different ranges

During a simulation I discovered an interesting phenomenon: Given you have 3 agents. 2 are uniformly distributed between [0,1] and one between [0,2]. The question is how often do the smaller agents ...
-1
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0answers
29 views

stochastic model [on hold]

I am trying to simulate a model using ssa for a selection of initial values and be able to discuss the results. can anyone let me know if my code make sense? Basically, it's a simple SIR model over ...
0
votes
1answer
19 views

Simulating a controlled dynamical system

I am try to simulate a controlled dynamical system of the form $$\dot{x}=f(x,\phi(x)),$$ where $\phi$ is the controller. To do so, I am using Octave (an open source version of Matlab). My commands ...
-2
votes
0answers
20 views

Simulation question [closed]

I have a simulation question that goes like this: Use Rejection method to find an efficient way to generate a random variable having density function $$f(x) = 0.5(1+x)exp(-x), 0 < x < \infty$$ ...
0
votes
1answer
16 views

Approximation and Monte Carlo simulation.

I am a bit up over my head here, I will present an argument and then I hope you guys will say if my reasoning is correct or what should be changed, ultimately I am hoping to say something qualified ...
-1
votes
2answers
39 views

Wrong simulation

I am simulating $(1+\eta)^{19}$ where $\eta$ is exponentially distributed with mean 0.15. I'm suppose to get on average 21 thousands. But my code below never output anything above 100. What am I ...
0
votes
1answer
39 views

Simple Monte Carlo simulation/approximation of 2 pair in a 5 card poker hand

I am very curious about simulation of an event where an estimating/sampling technique is used. In this example, the goal is to simulate a subset of all the roughly $2.6$ million $5$ card poker hands ...
0
votes
0answers
12 views

Individual particle tracking simulation

I want to do a simulation of a stochastic system. I have 4 types of cell, each will divide or die with a certain probability. Let's say : A-> A+A A -> A+B A -> A+C B-> B+B B-> die and so on... ...
0
votes
1answer
24 views

Distribution of hitting position of line by brownian motion.

What is known about the distribution of the hitting position of a line by a 2d brownian motion? I've tried to make some simulations of a 2d brownian motion where every computational step has a ...
0
votes
2answers
23 views

How to calculate the direction (of velocity of a ball) after collision with another ball?

Say I have two balls of same radius, in the 2-D Plane. So like a pool (billiard) game. I have the cue ball, moving with the velocity vector V, the magnitude is not important, so we only need an angle ...
3
votes
0answers
33 views

Maximize or find an upper bound of the function $kx^{k-1}\exp(-\mu(x^k-x))$

I was programming some random variable simulation using the acceptance-rejection method and I encounter with the Weibull$(k,\lambda)$ distribution. This random variable is posible to simulate with ...
0
votes
0answers
53 views

Water swallowing in Matlab

I want to simulate some water passing through a vertical cylinder in Matlab, and I would like to implement a 3d animation of it. I built the cylinder using the patch function, but I do not know how to ...
0
votes
0answers
19 views

Simulation Lévy process

I need to simulate a Lévy process from its characteristic triple $(\gamma,\Sigma,\nu)$ where $\nu$ is the Lévy measure. I know that I can simulate it by summing a brownian motion and a compound ...
1
vote
1answer
36 views

Simulate simple non-homogeneous Poisson proces

Consider a Poisson process whose conditional intensity is $$\lambda(t) = \alpha e^{-t}$$ starting at time $t=0$ for some parameter $\alpha>0$. I would like to simulate arrival/event/failure ...
0
votes
0answers
66 views

Estimation covariance of the Kalman filter state

I implemented Kalman filtering for a simplest 1D coordinate+velocity model. The prediction worked, but I wanted to estimate the prediction probability distribution. I.e. how likely it is that the ...
0
votes
1answer
38 views

How to simulate from a simple point process

Define a point process by the conditional intensity function $$\lambda^*(t) = \mu + \alpha \sum_{t_i < t} e^{-(t-t_i)}$$ where $\mu$ and $\alpha$ are positive parameters. I would like to ...
0
votes
0answers
10 views

Generating a given length sample and skewness whose normality is verified by one normality test but not by an other

I just want to generate 1 sample of length$=n>30$, |skewness$=S|<0.3$ and for which normality is not rejected by Shapiro wilk test of normality but rejected by Anderson darling test of ...
0
votes
0answers
13 views

spatial-partitioning based physical simulation

I've learnt that spatial-partitioning based physical simulation is kind of "approximate" computation. Is it because: since the whole space is partitioned into cells, and only the interactions of ...
1
vote
0answers
19 views

Stability of simulation of brownian noise

As I understand, Brownian noise can be simulated by the process $$x_{n+1}=x_n+R_n$$ where $R\sim U[-a,a]$. The expected value for $x_n$ is then $x_0$. But $\text{Var} x_n\to\infty$ as $n\to\infty$ ...
1
vote
1answer
53 views

Estimate arrival time of a ship given the average of the ships in a day in a Poisson Distribution

I'm working in a simulation of a Port where ships come to specific stations of the port. I already know that the average amount of ships is given by a Poisson distribution and the service time (On ...
1
vote
1answer
27 views

Simulation of orbiting bodies

I am writing a computer program to simulate orbiting bodies such as planets and stars. I wish to have a starting point in which a number of bodies are randomly scattered around a central heavy body. ...
1
vote
0answers
30 views

Distribution of phone calls during 24h

I would like to model the amount of phone calls at each time of the day. The phone calls should follow a poisson distribution and at 12:00 there should be the peak. So, semantically what I would like ...
-2
votes
2answers
58 views

Operations on distributions

Say we have two r.v X and Y which are independent and differently distributed ( for e.g X follows a bell curve and Y follows an exponential distribution with parameter $\lambda > 0$ What are the ...
0
votes
1answer
30 views

Simulation from cdf

Give a method for simulating from $$F(x) =\left\{\matrix{ \frac{(1-e^{-2x}+2x)}{3},& 0 < x < 1\cr \frac{3-e^{-2x}}{3}, & 1 < x < ∞}\right.$$ (Work out the pdf, and try to ...
0
votes
1answer
34 views

Calculate expectation under risk neutral measure: $\mathbb{E_Q}(\max(S-1,0))$

I am busy with a numerical simulation and I want the calculate the following expectation under the risk neutral measure: $\mathbb{E_Q}(\max(S-1,0))$. $S$ is some variable that I calculated using ...
1
vote
1answer
20 views

Proportion expected in a simulation

X and Y are independent random variables uniform taking values ​​in the sets {1, 2, 3} and {1, 2}, respectively. As can know by simulating the expected ratio for the pair $(X, Y)$ such that $X > ...
2
votes
1answer
25 views

Mean Value Function and CDF of Nonhomogeneous Poisson

Consider a nonhomogeneous Poisson process on $[0, T]$ with mean value function $m(t)$ for $t \in [0, T]$. Let $X_1$ denote the time of the first arrival. Show that $(X_1\,|\,N(T) = 1)$ has the ...
0
votes
1answer
25 views

Standard deviation shouldn't reduce?

I need to do a algorithm to calculate an integral via Monte Carlo Method, and for a purpose of simulation, I need to calculate the standard deviation of a sample generated in my program. My problem is ...
0
votes
1answer
51 views

Simulation - Find the maximum of a function with exponential decay

I need to run a program to calculate the integral of the following function with exponential decay $$t(x) = \exp(-Lx)(a\sin(bx) + d\cos(ex))$$ and for a simulation purpose, I need to find maximum of ...
1
vote
0answers
33 views

Forest fire simulation; analytically constructing a function for tree residual after fire

Consider a Cellular Automaton with an $n \times n$ grid, where each cell corresponds either to a tree or dirt. We assign a tree to cell $(i,j)$ by probability $p$. Next, we initiate a fire in some ...
2
votes
1answer
80 views

Proving that Markov Chain Monte Carlo converges

I am trying to understand how the very basic Markov Chain Monte Carlo approach works: We try to approximately calculate the expected value $E_{\pi(x)}[X]$ by drawing sequential samples from a Markov ...
1
vote
1answer
22 views

How to know when samples tend toward lowest number?

I am working on a computer simulation. In a perfect world, I only want to know what the minimum result value is from the simulation. (I have no a-priori knowledge about the range of numbers or their ...
1
vote
2answers
85 views

Calculate maximal island of ones in a matrix

I have came up with a problem involving matlab and matrices with entries 1 or zero. The matrix represents people in a footballstadium, doing a wave. If a person does the wave, he has a one in the ...
1
vote
0answers
77 views

Kalman Filter application to non-linear system.

I want to use the Kalman filter to have a better estimate of the state of a system which I know its equations of motion: ...
0
votes
0answers
35 views

Let X be exponentially distributed with mean 1. Let Y|X=x be exponential with mean x. You are interesting in estimating P($XY\leq3$).

I have some difficulties with homework. And I would be glad if you help me. Let X be exponentially distributed with mean 1. Let Y|X=x be exponential with mean x. You are interesting in estimating ...
0
votes
0answers
11 views

Is there a 'mild' product function?

I'm simulating an economy, each person has a list of integers representing the quantity of each resource they possess (for example: 5 water, 6 food, 2 education). From this I want to calculate ...
6
votes
1answer
69 views

Distribution of time spent above $0$ by a Brownian Bridge.

Let's say I have a Brownian motion, such that I know its value at time 0 (0) and time T (also 0). I am trying to evaluate the time spent above 0 between time 0 and T. Obviously I know that the ...
1
vote
0answers
36 views

simulate hitting time of Brownian motion

let's say I have a brownian motion $W_t$, and I know the value of $W_1$. Is there a way to simulate the hitting time of $W_t$ and a given function $f(t)$ ? For instance I know that if $f(t)$ is a ...
0
votes
0answers
146 views

How to count discarded entities in a FIFO queue using Simulink?

I'm trying to model a single queue, single server simulation using Simulink in MATLAB, I've recently installed it and I'm pretty new. I've created a Time-Based Entity Generator (with an exponential ...
1
vote
0answers
37 views

Random graphs simulation

Reading the article "Emergence of scaling in random network, by Barabasi and Albert" I faced a lot of results obtained by simulations of the A-B random graph model. I always wanted to do such ...
0
votes
0answers
15 views

interpolation linear for a sample path

I am looking for a couple of references: interpolation linear for a sample path of Brownian Motion
0
votes
1answer
19 views

Determining simulation threshold

Let's suppose we have some sort of game (for instance tic-tac-toe) with a limited amount of moves. I want to simulate that game, and with that I will use a random number generator (RNG) to calculate ...
0
votes
0answers
37 views

Are my estimates of parameters of geometric brownian motion correct?

I wrote a simulation of a geometric Brownian motion which works like this: $t_i - t_{ i-1 } \sim Exp(\lambda )$ $Z_i \sim N(0,1)$ $Y_i \sim e^{ \sigma \sqrt { t_i - t_{ i-1 } } Z_i +\left( \mu ...
0
votes
0answers
17 views

Coverage of squares by randomly putting circles with width following a Gaussian distribution

For some reason, I need to know the coverage of squares, if I put circles randomly on them. The radius of my circles follow a Gaussian distribution. For a better understanding see the attached ...
0
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0answers
55 views

Transition probability for time-homogeneous and inhomogeneous models

Consider the below matrices with four states - $0 , 1 , 2 , 3$ to be modelled by the means of a time-inhomogeneous discrete-time Markov chain. It's assumed the transition probabilities remain constant ...
0
votes
1answer
195 views

R - generate sample that follows a geometric distribution

I'm having trouble coming up with an algorithm that generates a sample (X1,...,Xn) of size n, considering several values for n, where the random variable Xi – “number of trials until the first success ...
2
votes
3answers
880 views

How do I simulate a simple pendulum?

I have the equation of motion of a simple pendulum as $$\frac{d^2\theta}{dt^2} + \frac{g}{l}\sin \theta = 0$$ It's a second order equation. I am trying to simulate it using a SDL library in C++. I ...
2
votes
2answers
44 views

Analytic methods vs Monte Carlo (terminology)

What's the correct terminology to say "We can calculate the probability exactly using pure math, as opposed to Monte Carlo simulation"? Analytically sounds like we need Calculus, which we may not ...