All Questions
Tagged with simulation self-study
61
questions
3
votes
1
answer
71
views
How to show in R, using a simulation, that when sampling from a normal distribution, the sample mean and sample variance are independent
What is the best way to show that when sampling from a normal distribution, the sample mean and sample variance are independent?
I know the theory behind this result, I would like to show it using a ...
- 31
1
vote
0
answers
115
views
Tightness of rejection sampling
Hello. I'm studying the Monte Carlo Statistical Method textbook by Robert and Casella. I have a question about exercise problem 30 in Chapter 2. I've already solved parts (a)-(c), but I'm having ...
- 31
1
vote
0
answers
55
views
Understanding and simulating a classic linear regression model with fixed coefficients
I had used the GPT chat to ask some straightforward questions. However, one of the responses left me feeling quite confused. Currently, I am studying the classical regression model given by
$$y_t = ...
- 247
0
votes
1
answer
102
views
Auxiliary randomization and the generalized CDF inverse
I'm trying to solve Homework 4 from professor Ryan Tibshirani's class on "Advanced Topics in Statistical Learning" [pdf] at UC Berkeley. It deals with basic facts about CDFs and quantiles.
...
3
votes
0
answers
93
views
Generating uniformly distributed particles on a $n$-dimensional flat torus or periodic hypercube [closed]
I am trying to generate evenly distributed particles in an $n$-dimensional flat torus or a periodic hypercube.
I am not sure if any of this approaches suffices. Can you suggest alternative methods for ...
- 31
1
vote
1
answer
74
views
Defining censoring level in survival analysis
I'm conducting a simulation analysis using the Exponential, Weibull and Gompertz distribution. To get the times I'm using the table from Austin 2012.
But how can I define the censoring level to be ~...
- 59
2
votes
1
answer
352
views
Simulating AR(2) Process With Initial Conditions
Consider a system process given by $$x_t = -0.9x_{t-2} + w_t, \hspace{2mm} t=1,\dots n$$ where $x_0 \sim N(0,\sigma^2_0), x_{-1} \sim N(0,\sigma_1^2)$, and $w_t$ is Gaussian white noise with variance $...
- 331
4
votes
2
answers
598
views
How to simulate data of a random intercept effect model in R?
I want to simulate data of the following random intercept effect model in R
$$Y_{ij}=\alpha+\beta x_{ij}+u_{0,i}+\epsilon_{ij}$$
$$u_{0,i} \sim N(0,\tau^2)$$
$$\epsilon_{ij} \sim N(0,\sigma^2)$$
Here ...
- 521
1
vote
0
answers
41
views
Generating random variates knowing the density function
Let's consider a random variable that is following the distribution with the density function as below:
$$f(x) = \begin{cases} \sum_{i=1}^{\infty} 3.5i(0.3)^{i-1}e^{-5ix} & \text{for $x>0$} \\ ...
- 604
0
votes
0
answers
17
views
Calculating the sample cumulative distribution function for a Kolmogrov-Simulation test to examine the goodness of fit with given data [duplicate]
I have sample data for 'Times between successive crashes of a computer system' which is for a 6 month period and the data is given in hours.
The data in brief is : 1,10,20,30,40,52.....
I need to use ...
- 1
2
votes
0
answers
189
views
Monte Carlo integration with Control Variate not giving any variance reduction
Given $I=\int_{3}^{+\infty}\dfrac{1}{\sqrt{2\pi}}e^{-x^2/2} \, dx$, I want to use a Control variate function to reduce the variance of a simple Monte Carlo simulation to compute this integral. In ...
- 141
18
votes
3
answers
11k
views
Generating random points uniformly on a disk [duplicate]
I have to randomly generate 1000 points over a unit disk such that are uniformly distributed on this disk. Now, for that, I select a radius $r$ and angular orientation $\alpha$ such that the radius $r$...
- 357
2
votes
1
answer
344
views
Is constructing a simulated model for a fixed SNR possible in binary regression?
When studying variable selection techniques like step-wise regression and the LASSO, a few studies employ a signal to ratio measure in order to control the amount of variability in a simulation. ...
- 1,622
0
votes
1
answer
405
views
Data generation process from an given regression model and monte-carlo experiment in R
I want to generate data in R to solve the following problem:
Consider the following Data Generating Process (DGP)
$Y_i = β_0 + β_1 · X_i + β_2 · Z_i + u_i$ ,
where $β_0 = 0.75$, $β_1 = 0.50$ and $β_2 ...
- 13
3
votes
1
answer
52
views
Book recommendations on how to conduct simulations in the context of OLS and Structural Equation Modelling
The title really says it all. Does anyone have any recommendations for well-written books, preferably with plenty of examples, on how to conduct simulation studies in the context of OLS and Structural ...
- 2,292