Linked Questions
36 questions linked to/from How does the inverse transform method work?
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"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 ...
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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?
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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 ...
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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.
https://math.stackexchange.com/questions/868400/showing-that-y-has-a-uniform-distribution-if-y-fx-where-f-is-the-cdf-of-contin
But in that case since $...
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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 ...
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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:
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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 ...
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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 ...
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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 $(0,1)$ ...
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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 ...
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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 \...
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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 ...
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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 ...
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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 ...
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Why compare with uniform distributed values in metropolis-hastings?
I'm a new starter in metropolis-hastings algorithm, having a problem in understanding its implementation of acceptance step:
min{1, f(Y)/f(x)}
I understand ...
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