Linked Questions

0 votes
2 answers

"Intuitive" Understanding of the Probability Integral Transform [duplicate]

I am trying to find a more "intuitive" understanding of the Probability Integral Transform (for the sake of better understanding Copula Models). As far as I understand, the Probability ...
stats_noob's user avatar
1 vote
0 answers

How to get Normal(Gauss) distribution from unifrom distribution? [duplicate]

I need to use rand(uniform distribution) function in matlab to generate a gaussian/normal distribution. What is the best way to do this?
bcan's user avatar
  • 121
0 votes
0 answers

The inverse cumulative distribution function evaluated at Halton draws [duplicate]

Sandor and Train (2004, Quasi-random simulation of discrete choice models) mention that "A randomized Halton sequence is a set of draws from the uniform distribution. To obtain draws from density ...
Snoopy's user avatar
  • 513
0 votes
0 answers

If $Y=F(X)$ is $U[0,1]$ where $F$ is cdf of continuous $X$ then shouldn't its plot be rectangular? [duplicate]

I understand the analytical proof given here. But in that case since $...
pavybez's user avatar
  • 59
55 votes
3 answers

Help me understand the quantile (inverse CDF) function

I am reading about the quantile function, but it is not clear to me. Could you provide a more intuitive explanation than the one provided below? Since the cdf $F$ is a monotonically increasing ...
Inder Gill's user avatar
11 votes
4 answers

How to generate a $\pm 1$ sequence with mean $0.05$?

I know how to generate a $\pm 1$ sequence with mean $0$. For example, in Matlab, if I want to generate a $\pm 1$ sequence of length $10000$, it is: ...
Ka Wa Yip's user avatar
  • 215
13 votes
2 answers

How do I sample from a discrete (categorical) distribution in log space?

Suppose I have a discrete distribution defined by the vector $\theta_0, \theta_1, ..., \theta_N$ such that category $0$ will be drawn with probability $\theta_0$ and so on. I then discover that some ...
Josh Hansen's user avatar
13 votes
2 answers

Efficiently sampling a thresholded Beta distribution

How should I efficiently sample from the following distribution? $$ x \sim B(\alpha, \beta),\space x > k $$ If $k$ is not too big then rejection sampling may be the best approach, but I am not ...
user1502040's user avatar
14 votes
2 answers

What is meant by "Laplace noise"?

I am currently writing algorithm for differential privacy using the Laplace mechanism. Unfortunately I have no background in statistics, therefore a lot of terms are unknown to me. So now I'm ...
Axolotl's user avatar
  • 143
18 votes
1 answer

Advantages of Box-Muller over inverse CDF method for simulating Normal distribution?

In order to simulate a normal distribution from a set of uniform variables, there are several techniques: The Box-Muller algorithm, in which one samples two independent uniform variates on $(0,1)$ ...
user2350366's user avatar
6 votes
2 answers

Programming inverse-transformation sampling for Pareto distribution

I am having trouble deriving a formula, and running a simulation with its distribution. The Pareto distribution has CDF: $$F(x) = 1 - \bigg( \frac{k}{x} \bigg)^\gamma \quad \quad \quad \text{for } x \...
John Huang's user avatar
5 votes
1 answer

How does the inverse transform method work in discrete r.v.?

In this question How does the inverse transform method work? it's mentioned the general procedure to generate r.v. U <- runif(1e6) X <- qnorm(U) X How ...
I likeThatMeow's user avatar
9 votes
1 answer

Generate random numbers from "sloped uniform distribution" from mathematical theory

For some purpose, I need to generate random numbers (data) from "sloped uniform" distribution. The "slope" of this distribution may vary in some reasonable interval, and then my distribution should ...
Robert's user avatar
  • 275
1 vote
1 answer

Generating random numbers from normal distribution via inverse uniform distribution

I would like to create a random number generator for the normal distribution via using a uniform linear congruential generator (on uniform distribution) and the inversion method. However, I'm getting ...
Wboy's user avatar
  • 157
5 votes
1 answer

How to find the Inverse Transform of the Gumbel distribution

How does one find the Inverse Tranform of the Gumbel distribution? Let $X\sim \text{Gumbel}(\mu,\beta)$ with scale parameter $\beta>0$. The CDF is then $F_X(x)=\text{e}^{-\text{e}^{-(x-\mu)/\beta}...
SecretAgentMan's user avatar

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