A vast area which includes generating results from computer models.

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2answers
29 views

Convergence rate of mean and standard deviation.

I have a random variable simulator with Normal distribution $(\mu,\sigma^2)$. I repeatedly conduction simulation. Each time, the simulation gives $N$ numbers $x_1,x_2,\ldots,x_N$. I use the $N$ ...
0
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0answers
10 views

Generate random variable with density function [on hold]

How can I generate a random variable that has the density function equal to $h(x) =\begin{cases} 0, & x \notin [0,1] \\ 1, & x \in [0,1] \end{cases}$ ?
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0answers
16 views

Is the result of a Monte-Carlo simulation of a continuous function and with continuous input distributions again continuous?

Is the result of a Monte-Carlo simulation of a continuos function and with continuos input distributions again continuous? Suppose, we have a continuos function $f$ and a number of continuous random ...
2
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0answers
41 views

What is the benefit of stochastic models over deterministic models? [duplicate]

I have posted a similar question earlier and I guess this sounds naive to all of you, but nonetheless let me just ask: Consider I have a simple and deterministic model $M$, with a number of input ...
1
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0answers
24 views

Test a law-of-iterated-logarithm-like result, with numerical simulation

I have a non-standard random walk $S_n$ for which the increments are not exactly independent (I could describe it, but it would be a totally different long and complex topic). I expect it to have ...
0
votes
1answer
53 views

Monte-Carlo simulation with sampling from uniform distribution

I used to work with Monte-Carlo simulations for a while. In my case, I generated random data for a variety of input parameters according to uniform distributions (with non-negative support), say for ...
3
votes
1answer
60 views

Numerical evidence of law of iterated logarithm (random walk)

The law of iterated logarithm states that for a random walk $$S_n = X_1 + X_2 + ... X_n$$ with $X_i$ independent random variables such that $P(X_i = 1) = P(X_i = 1) = 1/2$, we have $$\limsup_{n ...
0
votes
1answer
30 views

How do you calculate the correlation between the intercept's and beta's standard error in a univariate linear regression?

I am running a regression to predict a variable Y as follows: $Y=\alpha+\beta\times x+\epsilon$ I am trying to get a distribution of the expected value of Y given standard errors in the model ...
0
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0answers
11 views

The exact usage of Sequential Monte Carlo for distributions over time?

I have wondered the usage of Sequential Monte Carlos and it is used as an alternative to Kalman filter for example. However I wonder if this can be also used for simulating a distribution over time? ...
0
votes
1answer
38 views

Average of Monte Carlo simulations of continuous functions again continuous?

I hope the following question is clear: Suppose, we have a continuous functions $f:\mathbb{N}^2 \rightarrow \mathbb{N}$. Now, suppose we run Monte Carlo simulations on the function, where the input ...
1
vote
1answer
507 views

Simulation of a Gaussian process on $R^2$ with a stationary kernel using the Karhunen-Loève expansion

Assume $X(\omega, t) \sim \mathcal{N}(0, K(\cdot, \cdot))$ is a real-valued, centered Gaussian process on $R^2$, i.e., $X: \Omega \times R^2 \to R$. Let the covariance function of the process be ...
0
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2answers
58 views

What are numerical methods of evaluating $P(1 < Z \leq 2)$ for standard normal Z? [closed]

Let $Z \sim Norm(0, 1)$ and denote its PDF and CDF by $\phi$ and $\Phi$ respectively. Then, theoretically, $P(1 < Z \leq 2) = \Phi(2) - \Phi(1).$ However $\Phi$ cannot be expressed in closed form, ...
0
votes
3answers
49 views

Given a number '$N$' find how many how many numbers are there between $1$ to $N$ that doesn't contain the digit $3$?

You are given a number $N\le 10^{18}$. You need to find out how many numbers there exist in between $1$ to $N$, which doesn't contain the digit $'X'$ in it . Say $N = 5, X=4$ The answer is $4$. ...
1
vote
1answer
19 views

analytical hard sphere collision condition with periodic boundary conditions

Hello Stack Exchange Mathematics, I am curious if there is an analytical or efficient numerical solution for the collision of hard spheres in a rectangular unit cell with periodic boundary ...
0
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0answers
4 views

Block covariance

I generate a field ($n_x \times n_y$) with covariance structure (variogram). However, I have only access to an upscaled version of this field. I'm looking to simulate a field at the fine scale ($n_x ...
5
votes
3answers
191 views

Probability that a quadratic equation with random coefficients has real roots

Consider quadratic equations $Ax^2 + Bx + C = 0,$ in which $A, B,$ and $C$ are independently distributed $Unif(0,1).$ What is the probability that roots of such an equation are real? This problem is ...
1
vote
1answer
24 views

Simulation of the variance of a typical waiting time W(q) in a queue

Write a computer programme that by means of stochastic simulation finds an approximation of the variance of a typical waiting time W(q) (in the queue) before service for a typical customer arriving to ...
1
vote
1answer
29 views

Klein Bottles in the Levine traffic model

The Biham–Middleton–Levine traffic model has recently fascinated me. I started learning about it on the Wikipedia Page found here. One way to run this simulation is on a Klein bottle surface. When ...
2
votes
1answer
32 views

Managing a bond fund: Simulating the maximum of correlated normal variates

Two rating agencies score the safety of bonds in a particular population on separate standard normal scales. Because the two agencies take some of the same factors into account in their ratings, the ...
5
votes
1answer
71 views

Looking for good books about simulating stochastic processes.

Yes, like the title says im looking for books about simulating stochastic processes. If they are using R in the book its great. If they are using matlab its good too or if they are just describing ...
3
votes
1answer
47 views

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?
3
votes
1answer
60 views

Computational methods for the limiting distribution of a finite ergodic Markov chain

We wish to show what can be discovered about the limit of a finite, homogeneous, ergodic Markov Chain $X_1, X_2, \dots,$ using simple methods of computation and simulation. Specifically, consider the ...
5
votes
2answers
78 views

Determining number of randomly picked people

Firstly I want to put big disclaimer here. This particular problem is a smaller part of my homework. Since even after discussion with my fellow classmates we are not sure how to handle it we decided ...
0
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0answers
34 views

Guesstimating a probability distribution from plots, tails and moments

While working on a recreational / experimental math problem I have simulated some data and would like to find out the underlying distribution. For the moment I will consider the process which led to ...
1
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1answer
56 views

How to simulate visits to a transient state of a Markov chain.

Consider a discrete-parameter Markov chain $\{X_n, n ≥ 0\}$ with state space $E$, transition probability matrix $P$ and initial-state probabilities $p(0)$ given by $E = \{0, 1, 2, 3\}$, P = ...
2
votes
1answer
62 views

Find a>1 s.t. $a^x = x$ has a unique solution

What $a$ makes $\{x\mid a^x = x\}$ a singleton? $$(1.4444)^x - x \le 0 \tag 1$$ has real solutions. $$(1.4447)^x - x \le 0 \tag 2$$ has no real solutions. I guess $1.4444 < a < 1.4447$ I ...
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0answers
22 views

Quantile lines of stationary process

Quantile lines of any stationary process are parallel and constant. But for different procesess I've obtained different behavior of quantile lines. First case was process after Lamperti transormation ...
2
votes
1answer
50 views

$M/M/2/4$ simulation of the probability that the queue gets full during first $10$ time units.

Let $X(t)$ denote the total number of customers at time $t \geq 0$ in an $M/M/2/4$ queuing system in steady-state (/started according to its stationary distribution) with Poisson arrival process with ...
1
vote
1answer
34 views

Simulation of Brownian motion and white noise.

Let $\{W(t)\}$, $t≥0$ be a Wiener process with $ σ^2 = \operatorname{Var}\{W(1)\} = 1$. For a real constant $ε > 0$, consider the differential ratio process $∆ε = \{∆ε(t)\}$, $t>0$ given by ...
0
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3answers
2k views

Simulation of 2-dimensional Brownian motion

I am trying to simulate (for the first time) a 2-dimensional SDE, in Matlab. $$dX(t)=F(t,X(t))\,dt + \sigma(t,X(t))\,dBt$$ I have no problem using the Euler-Maruyama method in the one dimensional ...
2
votes
3answers
120 views

Find expected value of time to reach a state in Markov chain, by simulation

Consider a time homogeneous Markov chain $ (X_n)_{n=0} $ with state space $E$, initial distribution $p(0)$ and transition probability matrix $P$ given by $E = \{0, 1, 2\}, p(0) = [1\;\; 0\;\; 0]$ and ...
1
vote
1answer
63 views

Optimal strategy for unlocking Cho'gall (probability intuition question)

Right now there is an event occurring in Heroes of the Storm where a special hero (Cho'gall) is unlocked if you play with another player currently playing that hero. I ran into a bit of an intuition ...
1
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1answer
21 views

how to simulate from joint distribution by conditioning

I have a simple question about simulation from joint distribution. Suppose $(X,Y)$ has a joint distribution $p(x,y)$, and we know the marginal of $Y$, $p(y)$, and the conditional distribution of $X$ ...
35
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3answers
3k views

Why is this coin-flipping probability problem unsolved?

You play a game flipping a fair coin. You may stop after any trial, at which point you are paid in dollars the percentage of heads flipped. So if on the first trial you flip a head, you should stop ...
8
votes
1answer
333 views

Expected travel of random walk in arbitrary game with multiple payouts

As explained here, the average distance or 'travel' of a random walk with $N$ coin tosses approaches: $$\sqrt{\dfrac{2N}{\pi}}$$ What a beautiful result - who would've thought $\pi$ was involved! ...
0
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1answer
61 views

Does elevator passenger's wait time depend on floor (on average)?

Assume a skyscraper and a passenger that only uses the elevators. All elevators go from the first to the last floor. Does the length of time the passenger wait (on average) depend on the floor? (i.e. ...
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0answers
48 views

Does elevator passenger's wait time depend on floor (in average)?

Assume a skyscraper and a passenger that use only elevator (not stairs). Each elevator's range is from the first to the last floor. Does elevator passenger's wait time (in average) depend on floor? ...
0
votes
1answer
34 views

Euler-Maruyama simulation of an SDE

The Euler-Maruyama method for the following SDE \begin{align} dX_{t} &= -\lambda X_{t}dt + \mu dW_{t}\\ X_{0}&=x>0 \end{align} where $\lambda,\mu$ are given constants, is (according to ...
1
vote
1answer
26 views

Mistake in generating random numbers - no irrational ones

Hi I just wondered if the probability densities have to be corrected when using them on a PC since the number representation is not at all continuous. So we cant simulate any irrational numbers and ...
2
votes
0answers
25 views

Calculating integral with antithetic variables

Use simulation with antithetic variables and find $$\int_{-\infty}^\infty \int_0^\infty \sin(x+y)e^{-x^2+4x-y} \, dx \, dy.$$ so, my question and doubt is how struggle with the infinite limit ? It ...
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0answers
19 views

Sketch the reachability graph for the Petri net model

Petri net for traffic light Sketch the reachability graph for the Petri net model of the two traffic light system shown above. I know the starting is (1, 0, 0) but I'm not sure how to draw it and ...
0
votes
1answer
26 views

simulate problem probability

you have x children and you want to buy C candies, which you want to give to them in such a way that each child is equally likely as any other child to get no candies, one candy or maybe all the ...
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0answers
38 views

Self learning complex systems modeling

I am currently a senior studying mathematics. My program is heavily focused on pure maths, however, my interests lie in the area of applied mathematics. Specifically, I am interested in the study of ...
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0answers
21 views

Generate a sequence of Poisson random variables

I have to generate a sequence of $n$ random Poisson variables with rate $λ=122$. I used this algorithm: STEP1: $λ=122, i=0, p=e^{-λ}, F=p, n>0\in N $ STEP2: Generate a psudorandom number ...
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0answers
20 views

Generate a whole random variate uniformly distributed

I have to describe an algorithm to generate a whole random variate $X$ uniformly distributed on the interval $[a,b]$ where $a,b\ge0, b>a$ I used the inverse trasform algorithm: STEP1: Generate U ...
0
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1answer
14 views

Required number of simulation runs

I have the following problem: One wants to estimate the expectation of a random variable X. A set of 16 data values (i.e. simulation outputs) is given, and one should determine roughly how many ...
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0answers
48 views

interarrival time

I am trying to model the arrival rate (delay between the arrivals) of the cars in my city. I have some real data with the resolution of one minute. For example, Number of counted cars at position x at ...
1
vote
1answer
72 views

What does the time-reversibility of Verlet (or other) integration mean?

What does the time-reversibility of Verlet or any other integration method mean? The wikipedia article about it is very complex, unclear and confusing. And how can I determine whether a method is time ...
0
votes
1answer
113 views

Simulate random data with a given probability density function

Let $(X, Y)$ be a random vector with density $f(x,y) = c I_A(x,y)$ where $A=\{(x,y): 0<x^2<y<1\}$. $I_A$ is a characteristic function. I need to simulate random data with this pdf. It is ...
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2answers
34 views

In writing a simulator to simulate an experiment that rolls 2 dice and checks if the sum of the 2 rolls is less than or equal to a given value.

Is it better to use 2 independent random number generators or one array of size 36 that holds the sample space(of all possible sums) and use one random number generator to choose from this arry. ...