Questions tagged [random-generation]
The act of generating a sequence of numbers or symbols randomly, or (almost always) pseudo-randomly; i.e., with lack of any predictability or pattern.
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Generating a random number with CDF $P(X \leq c) = 1-1/c$ in the interval $(1, + \infty)$. using uniform distribution
I have a uniform number generator in ($0, 1).$ I want to generate a random number with CDF $P(X \leq c) = 1-1/c$ in the interval $(1, + \infty)$. I know I should apply the inverse of my function to ...
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Is there a law or theorem related to occurrence of an event with highest probability in a population with infinite size?
Assume, we have a key that appears in either of the three rooms randomly (red room, blue room, and green room). We have the following probability distribution:
...
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Random Walk and Moving Average for Stock Market Model
I model a stock price with a completely random walk:
In each step I multiply the price with normal distributed random number with an mean of 1.
Then I compute a signal, which is True if the moving ...
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Question about the inversion method for simulation of random variables [closed]
In the method called inversion we have :
Let $U$ ~ unif(0,1) denote a uniform random variable on $(0,1)$.
Then : $\mathbb{P}(F^{-1}(U))$ = $\mathbb{P}(U \leq F(x))=F(x)$
so $F^{-1}(U)$ has ...
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How does one sample from a gaussian distribution without a library? [duplicate]
I am looking to write a program that generates samples from a gaussian distribution with a certain mean and standard deviation. I am not allowed to use any library except a random number generator. Is ...
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Bootstrapping CI around variance ratio from random regression model
I am interested in the ratio of random slope variance from a random slope and intercept model. I fit the model using lme4 as
...
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Generate numbers between 0 and N in a random order guaranteeing uniqueness with efficient memory cost [closed]
I'm trying to think of a method i could use to generate the random numbers between 0 and N in a random order and with uniqueness that would use the smallest footprint of memory at the beginning and ...
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How many numbers can I generate and be 90% sure that there are no duplicates?
Suppose I am generating random 4-digit numbers. Obviously there are 10,000 possible numbers, but the chances are I will get a duplicate long before I generate that many.
Can anyone explain how I would ...
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Sampling from Gaussian Process
I am learning the Gaussian process and feel confused about how three lines were generated in Fig 2.2(A) in the book "Gaussian Process For Machine Learning". As described by the author: "...
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Drawing numbers using the CDF
Say I have a (generally high-dimensional) random variable $X$ with known, continuous CDF $F(X)$.
Is there a good algorithm for drawing values of $X$ that doesn't require that I calculate the joint ...
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Drawing random numbers with quadrature
In a comment on this question, the user 'probabilityislogic' says "No, not MCMC this thing! Quadrature this thing! only 2 parameters - quadrature is the "gold standard" for small ...
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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 ...
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How to generate from this distribution without inverse in R/Python?
I am working with a distribution with the following density: $$f(x) = - \frac{(\alpha+1)^2 x^\alpha \log(\beta x)}{1-(\alpha + 1)\log(\beta)}$$ and CDF $$\mathbb{P} (X \leq x) = \int_0^x - \frac{(\...
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Testing relationship between exponential and beta distributions using R
If X ~ Exp(3), Y ~ Exp(1) and h = X / (X + Y) then h ~ beta(1/3, 1) and E(h) = 1/4.
But when I draw random deviates using the following R code, I find mean(h) ≈ 0.324 and the histogram doesn't ...
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Sampling from a distribution function $g_{x}$ that will follow $f_{x}$
I am using acceptance-rejection sampling to sample random variable $x$ according to distribution $f(x)$. The steps I followed are
First generated uniformly distributed random variable $x$ from 0 to $...
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How to generate a standard normal distributed time-series with a given ACF
I want to generate a standard normal distributed time-series. In addition the ACF of my timeseries should match a desired ACF. I have given lags 1 to 30 with the corresponding ACF-values. For further ...
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Relaxed magic-square generator distribution
This question is about a magic square generator, "relaxed" because
it's only about one vector (row) in the square independent of all other rows;
the individual elements are continuous and ...
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Generating uniformly distributed random solutions of a linear equation
Given $n+1$ variables $p_0, p_1, \ldots, p_n$ defined over $\mathbb{R}^{+}$ so that $\sum_{i=0}^np_i=1$, and given a real number $1<x<n$, I want to generate random solutions of the equation so ...
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How to generate uniform distributed samples with given auto-correlation function
As I mentioned in the question title, I want to generate specific uniformly distributed samples.
I need them to model a real world scenario. For my real data, I estimated a function, which ...
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Control Chart: Nelson alternating rule
The Nelson rules for control charts describe patterns, which are "special" and need our attention. One of these rules is the "alternation rule". According to Nelson it is "...
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random number generation of truncated multivariate normal distribution
I want to generate random numbers from truncated multivariate normal distribution specified as follows:
$ \begin{bmatrix}
Y \\
X
\end{bmatrix} \sim N
\begin{pmatrix}
\begin{bmatrix}
\mu_Y \\
\mu_X
\...
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Random number generator for non-central chi-squared with non-integer dimension
Does someone know of a random number generation algorithm for a non-central chi-squared distribution with a non-integer dimension?
PS By algorithm, I am interested in the detailed procedure or ...
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Numerical Stability when Inverse CDF Sampling from Truncated Density
Let $f(x)$ be the pdf of a random variable that we want to truncate to the interval $[a,b]$ and then sample from it. Let $F(x)$ denote the corresponding cdf. We can use inverse cdf sampling and ...
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Suppose $f: \mathbb{R}^n \to [0, 1]$ is known, how to sample $x \in \mathbb{R}^n$ such that $f(x)$ follows uniform distribution? [closed]
Suppose $f: \mathbb{R}^n \to \mathbb{R}$ is known, where evaluation and gradient computation is easy. How can I sample $x \in \mathbb{R}^n$ such that $f_x \in \mathbb{R}$ follows uniform distribution? ...
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How many toss a coin attempts required so the noise is always less than 1%?
I don't know what is it in statistic term, but I will say it the noise.
Noise is defined as absolute difference between real percentage result after experiment and ideal probability.
The question is ...
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Generate two random correlation matrices which share equal correlations
My setting is, I want to simulate a data set in two conditions, e.g. control and disease. I want them to share mostly the same correlations except some should be different to simulate a "signal&...
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Generating random variables from a mixture of Normal distributions and Exponential distribution using composition method
How can I sample from a mixture distribution in particular a mixture of Normal distributions and Exponential distribution in R using composition method?
For instance if I want to sample from:
$0.3\...
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Perfect sampling and inverse transform sampling
Firstly, looking at the discussion https://math.stackexchange.com/questions/241315/three-ideas-of-perfect-sampling, the term "perfect sampling" does not seem adequate, since there are ...
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How can I find the k-th smallest element of my list of random numbers? [closed]
I have generated exponential random numbers using x <- rexp(1000,1) with set.seed(1). I can look at them using ...
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Element-wise comparisons of sorted subsets of random numbers yield nonrandom results
Say we have a random number generator. It generates 2000 numbers that we put in two arrays, 1000 numbers each. Like this (here shorter arrays used to illustrate the point):
[4, 20, 5, 6]
[7, 21, 3, 3]
...
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What is B. D. Ripley's method of seeding the Mersenne-Twister RNG?
R's documentation behind ?runif states that the default RNG is
"Mersenne-Twister": From Matsumoto and Nishimura (1998); code updated
in 2002. A twisted ...
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Pseudo-dice probability distribution
Given the following data, is there an algorithmic way to generate a probability distribution?
Data: min, max, and average results of "die".
Known Trend: results will always be weighted ...
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Random sampling from a super level set
I have a random sampler from a region $X$. Suppose, I have a function $f: X \to \mathbb{R}$, where I can explicitly evaluate $f(x)$ and also obtain the gradient $\frac{\partial f}{\partial x}$ easily (...
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Generating random variable which has a power distribution of Box and Tiao (1962)
Box and Tiao (Biometrika 1962) use a distribution whose density has the following form: $$f(x; \mu, \sigma, \alpha) = \omega \exp\left\{ -\frac{1}{2} \Big\vert\frac{x-\mu}{\sigma}\Big\vert^{\frac{2}{(...
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Why doesn't R use Inverse Transform Sampling to sample from the Exponential Distribution?
I was reading this question about the algorithm that R uses to sample from the Exponential($\lambda$) distribution. It looks like R uses the Ahrens-Dieter algorithm to sample from the exponential ...
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Using KDE to approximate a Price vs Quantity curve
I am trying to approximate Price-vs-Quantity (P-Q) curve of a dynamic product (think Hotels, Airlines etc). As you can imagine, if you take a hotel property, the price of rooms (assuming the same room ...
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How to simulate artifical data for multinomial regression? [duplicate]
I want to use some predictors (for example, $x_1$ and $x_2$ below) to simulate the multinomial outcome (for example, with 3 levels).
Below are the codes I found in another question regarding ...
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Creating a random sparse precision matrix?
In my current project, I want to create a random sparse precision matrix $\boldsymbol{P}=\boldsymbol{\Sigma}^{-1}$ (the inverse of a covariance matrix $\boldsymbol{\Sigma}$). My current procedure ...
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how to sample two random variables from different distributions and requiring one is always larger than the other
I know one way is to sample A and B independently and then reject the samples where A<B. But I wonder if there is an easier method?
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Draw random numbers from finite mixture model
Setup
Let X follow a fininte mixture model with density
\begin{equation}
f=\lambda f_1+(1-\lambda) f_2
\end{equation}
Where $f_1$ and $f_2$ are both log-normal densities with parameters $(\mu_1, \...
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Why is it difficult to sample from a multivariate distribution? [closed]
The Monte Carlo Markov Chain method requires sampling from a multivariate distribution. This is because the Markov Chain process requires dependent draws. See 1:55 at https://www.youtube.com/watch?v=...
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Sphere Point Picking
As explained here, sphere point picking can be performed using the easy formula
$x$ = $\sqrt{1-v^2}\cos\theta$
$y$ = $\sqrt{1-v^2}\sin\theta$
$z$ = $ v$
where $\theta\in [0, 2\pi]$ and $v \in [-1,1]...
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Generating sample data from a specified model
I am reading a book on longitudinal correlated data analysis available in https://www.taylorfrancis.com/books/mono/10.1201/9781420035285/generalized-estimating-equations-james-hardin-joseph-hilbe
In ...
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How much randomness is required for Gibbs sampling?
I am attempting to parallelize a program that executes hundreds of calls to Mallet's getSampledDistribution method, which is essentially an execution of Gibbs sampling over a topic distribution which ...
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Python/numpy - conditional sampling of variables, distribution of subsequent value is based on result of previous value
I am trying to generate a random sample of multiple variables which are loosely related to each other. Meaning that "allowed" values of some variables depend on the value which is set for ...
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How can I generate random observations from a concrete copula?
Let us assume that we have two continuous random variables $X$, $Y$, with known distributions (not necessarily normal), connected/related via a concrete copula.
What is a procedure to generate random ...
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Generating multivariate random variable with normal and exponential marginals
I have a collection of data points of the form $[U, V, X, Y]$, where $U$ ~ $N(\mu_1, \sigma_1)$; $V$ ~ $N(\mu_2, \sigma_2)$; $X$ ~ $exp(\lambda_1)$; and $Y$ ~ $exp(\lambda_2)$, and I am looking to ...
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Correlation matrix from pairwise correlations with specified structure
I need to simulate multivariate normal samples with a pre-specified correlation structure. The structure is such that the bigger the (GPS) distance between two points, the smaller the correlation (...
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How to weight probabilites of getting sampled depending on the frequency of occurrence?
Unfortunately I'm struggling to describe my problem mathematically. I have 2000 strings, many of which are repeated. Now I want to write a 'random' sampling algorithm that produces 100 samples out of ...
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Variance of the sum of multiple random number generators
Let's assume I have "n" random number generators, each one has a different variance value, but has the same mean value, zero.
If I generate "n" random numbers with these generators,...
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