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3
votes
0answers
26 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
44 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
17 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 ...
0
votes
0answers
35 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
37 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
9 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
45 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
25 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
29 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
28 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
28 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
19 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
23 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
19 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
38 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
29 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 ...
1
vote
1answer
70 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
72 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
66 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
34 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
67 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
30 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
127 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
16 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
votes
0answers
52 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
101 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
728 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
42 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 ...
1
vote
1answer
36 views

Question about the Monte Carlo Algortihm

I was reading the Monte Carlo algorithm for finding the area under a curve, say $y=f(x)$. The algorithm considers, $0\le f(x)\le M$ over the closed interval $a\le x\le b$. My question is,that why is ...
0
votes
0answers
29 views

Simulation of a Bidimensional Fractional Brownian motion

I would like to simulate and understand the simulation of a bidimensional fractional Brownian motion (I would like to try and use it to simulate terrain in a 3d game I am developing), but I cannot ...
1
vote
1answer
57 views

Calculating cumulative Markov Chain outcomes

I have a Markov process, with 2 possible states (1 or 0) and a transition matrix P. State at time t=n is determined by x0*Pn. As n goes to infinity, xn goes to the steady state vector, q = [q1 q2]. ...
0
votes
0answers
17 views

Monte Carlo by point or by interval

Say I compute monte carlo output from input scenarios. Input are discrete time series. I choose time series as an example to make the problem more obvious - this could be also any curve. Computation ...
0
votes
0answers
30 views

Determine whether intersecting sphere moves towards cuboid?

I am programming a physics simulation in which I check every frame of a sphere intersects a cuboid. If it intersects, I want to check if the sphere moves "towards" the cuboid in a sense. If it does, ...
0
votes
1answer
31 views

Finding variance .

Suppose that $f : [0, 1] → [0, 1]$ and we wish to estimate $$I = \int_{0}^{1} f(x) dx$$ Using the hit-and-miss method, we obtain the estimate $$\hat I_{HM}=\frac{1}{n}\sum_{i=1}^{n}X_i$$ where ...
0
votes
1answer
82 views

Finding Area and probability[ hard nut to crack].

Suppose that $X$ and $Y$ are iid uniform distribution with $U(0, 1)$ random variables. (a) What is $\mathbb P((X, Y ) ∈ [a, b]×[c, d])$ for $0 ≤ a ≤ b ≤ 1$ and $0 ≤ c ≤ d ≤ 1$ ? What is $\mathbb ...
0
votes
1answer
138 views

Plot the cdf and simulate a random variable (rv) with this cdf using the inversion method.

Consider the continuous random variable with pdf given by: $$f(x) = 2(x − 1)^2;\quad 1 < x ≤ 2$$ $$f(x) = 0;\quad \text{otherwise}$$ Plot the cdf for this random variable. Show how to simulate ...
0
votes
1answer
30 views

Congruential Generators.

Find all of the cycles of the following congruential generators. For each cycle identify which seeds $X_0$ lead to that cycle. $$(a). X_{n+1} = 9X_n + 3\mod 11$$ $$(b). X_{n+1} = 8X_n + 3\mod 11$$ ...
1
vote
1answer
47 views

Simulating Poisson distribution

I'm wondering if it is possible to simulate the Poisson distribution using the Alias Method, because we suppose to use this method for discrete random variables with finite support. So I think finite ...
1
vote
1answer
79 views

How to Prove by definition, the given process is a Markov Process?

Define the process Xt by X0 = 1, and for t = 1, 2, . . . Xt = { uXt-1, with probability p, { vXt-1, with probability 1-p where 0 < v < 1 ...
0
votes
0answers
22 views

Discrete models of 2 dimensional wave propagation

Usually most 2-d dimensional propagator waves are modeled by some general equation such as d/dt^2 = laplacian; However, if discretized, this sometimes only gives off (x,y) -> (x+1,y), (x-1,y), ...
1
vote
1answer
39 views

Simulation of typical cell in Poisson Voronoi tessellation

I would like to simulate a typical cell in Poisson-Voronoi tessellation model. I want to save the Cartesian coordinates of all vertices of the typical cell for each realization. How to do it? Thank ...