Questions tagged [sampling]
Questions about the statistical process of sampling from a population, in order to obtain information for use in statistical learning, estimation, hypothesis testing about some population or process.
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Sampling distribution output does not look like a continuous function
I made a random distribution using 2 dice rolls, the output usually collects most data around mean:
Then I try to do sampling of N sample size. While using sample size of N = 2 it looks more or less ...
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1answer
12 views
Sampling with and without replacement.
Prove that the probability of drawing a unit at any draw from a population of size N, remains same in without and with replacement sampling scheme.
I know how to prove that this probability is $\frac{...
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2answers
45 views
How to sample two values from a random variable X with the lesser to be a random variable Y?
The variable X has pdf $$f(x) = \frac18(6 - x)$$ for $$2 ≤ x ≤ 6$$
A sample of two values of X is taken. Denoting the lesser of the two values by Y, use the
cdf of X to write down the cdf of Y. Hence ...
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1answer
20 views
How can I calculate if my data is diverse
I conducted a survey in which the first question I asked students what year they were in. I want to check that I have a diverse amount of students (from many year groups) so I can say the survey data ...
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0answers
19 views
Sampling from Geometric distribution in constant time
I would like to know if there is any method to sample form the Geometric distribution in constant time without using $log$ which can be hard to approximate.
Thanks.
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17 views
Sampling distribution of a functional T
While studying the bootstrap method, I came across with the following definition of the sampling distribution of a functional T:
Let's say $X_1,...,X_n$ are i.i.d with distribution function $F$, then ...
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1answer
28 views
Approximate Probability With Beta Distribution
We are given a sample of 7 proportions for the percentage of cloud cover recorded at a set time every day for a week, where the sample mean is $\bar{x}=0.51$ and the sample variance is $s=0.3277$. We ...
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2answers
54 views
How do I evaluate (prove to myself) that a method for picking uniformly distributed values is correct?
To make this more specific, I show a broken procedure for generating random points in a circle and a correct (hopefully) procedure for generating random dates within an interval.
I'd like to be able ...
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1answer
34 views
Copula used for pseudo-random generation from continuous variables only?
I know multivariate pseudorandom generation from continuous distributions can be done using copulas and inverse transform sampling.
The question is if copula have application in "discrete" pseudo-...
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1answer
20 views
Finding the conditional distribution from empirical joint CDF
Suppose we are given a table containing the estimates of a discrete bivariate CDF $P(X_1\le x_1, X_2\le x_2)$ and also the known value of a realization of the first variable $X_1 = x_1$.
What are ...
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12 views
Magnitude spectrum of a sampled time continuous signal
I have a signal $x(t)=\cos(2 \pi 200 t)+2\cos(2 \pi 400 t)+\cos(2 \pi 600 t)$.
With sample frequency $F_s=1000 Hz$. How do I draw the magnitude spectrum of the sampled signal $x(n)$?
I've tried ...
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1answer
49 views
What curve represents random sampling sorted by frequency?
I perform a discrete random sample with a uniform distribution (such as drawing colored balls from a bag with replacement). I then plot the frequency that each color has been selected, ordered by ...
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1answer
30 views
How many items must be sampled to ensure normal distribution?
I was working on a problem that was dealing with proportions and it asked the following:
If a population proportion is believed to be $0.6$, how many items must be sampled to ensure that the sampling ...
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1answer
59 views
How can we approximate a function by sampling a distribution proportial to it and making a histogram of samples?
I've read the following (here on page 2):
Suppose that you want to approximate a function $f$. One way to do this is to produce a sampling distribution proportional to $f$ and then make a histogram ...
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0answers
42 views
Statistics - Stratified random Sampling
First, have a look at "Max Ft"'s answer to the following question:
Stratified Sampling for Variance Reduction--Need Intuition as to Why it Works
His answer makes sense for how stratified random ...
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1answer
21 views
Determine the number of samples needed with Bayes theorem
I have a simple sample statistic problem, but I am not sure that I solve it properly.
I have to enter many student marks to a test in an Excel table. After entering all $N$ marks, I want to know the ...
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0answers
15 views
Acceptance and rejection sampling.
The standard logistic distribution function F given by $F(x) = 1/(1+e^{-x}) , x$ is a real number.
How to generate a random sample of size 10000 using acceptance-rejection sampling using standard ...
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0answers
18 views
Samples from high dimensional distribution by exploiting the symmetry
I have a discrete 7-element random vector $\vec{X}$ with probability mass function $P_{\vec{X}}(\color{blue}{x_1,x_2,x_3},x_4,x_5,x_6,\color{red}{x_7})$ that has a symmetry in its certain components.
...
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3answers
36 views
Expected number of tries to choose x unique values
it's been a long time since I've dealt with probability so I thought I would ask here. I'm sampling elements independently and uniformly and with repetition from a population. Given that the ...
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1answer
22 views
Proof Random Sampling Interview
Got this algorithm in an interview.
To prove that the algorithm randomly shuffles the array.
The random sampling algorithm works as follows:
...
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0answers
26 views
N dimension random distribution with constraints
I am trying to draw $M$ random/semi-random numbers in $N$ dimensions applying some constraints. For instants I have a method that "selects" only the right points, but I am sure that it can be done ...
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0answers
14 views
Divergence between Probability Distributions from Samples via the Chamfer Distance
Suppose I have two probability distributions $P$ and $Q$. I want to compute a divergence/distance between them. I do not have access to their densities, but I can draw samples $x\in D \subset \mathbb{...
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22 views
Hogg Intro to Mathematical Statistics Sufficient Statistic Notation Question
When introducing the notation of a sufficient statistic, Hogg uses a peculiar sort of notation at the bottom of page 381 of the 7th edition textbook: given the statistic $$Y_1 = u_1(X_1,X_2,...,X_n)$$ ...
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20 views
How to implement a Metropolis Hastings step
I am having trouble implementing a Metropolis Hastings step in a Gibbs sampling problem. The following code was taken from here.
Details: It is a capture recapture study, with seven total draws from ...
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1answer
60 views
What is the mathematically appropriate and concise way of writing a constant added to a random number?
Let $x$ be a constant in $\mathbb{R}$.
Let $y$ be a random number that is generated according to a certain probability distribution.
I want to make the sum
$$x + y$$
However, I am not sure how to ...
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1answer
31 views
How to sample from a reconstructed pdf
Suppose, that we have a process that generates events. Subsequently these events are recorded and stored in a histogram. Say we have a source that emits particles and subsequently a histogram is build ...
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0answers
9 views
Hamiltonian monte carlo sampling : Energy Histogram vs Sample Histogram
I'm using HMC to sample from an N-d Gaussian. So the PDF is that of a multivariate normal distribution. HMC requires an energy function and its gradient. The library I'm using, maximizes the ...
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0answers
12 views
population distribution & sampling distribution [closed]
What is the difference between the population distribution of a random variable X and the sampling distribution of a random variable that is a sample statistic?
This is a question I got from my ...
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0answers
4 views
How to come up with variance for estimators?
I know that the variance is calculated with $Var(X) = \frac{1}{N} \sum^N (X_i - \bar{X})^2$
However, how do I come up with/derive variance formulas for e.g. the mean for different sampling methods.
...
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0answers
14 views
Hypergeometric distribution with heterogeneous sampling probabilities
I have been trying to find a proper framework for finding the corresponding generalization of the hypergeometric distribution when the sampling probability from the total items $N$ is not uniform.
...
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0answers
10 views
Least square estimate for post-stratification sampling
enter image description here
I figured out via the normal linear regression method that Beta0 hat = ybar - Beta1 hat xbar. But I am not sure how to find out the least square estimate for Chat. Is ...
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19 views
Finding the bias of an estimator
Consider the following model:
$$
y_i = a + b x_i + c z_i + w_i,
$$
where $a,b,c$ are unobserved fixed parameters, $x_i$ and $z_i$ are fixed in repeated samples. Assume also $\mathrm{E}[w_i] = 0$ for ...
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1answer
23 views
probability of extracting predefined k elements out of N in V extractions with replacement.
I have a set of $N$ elements from which I do $V$ extractions with replacement.
Given a subset of size $k$. What is the probability that all the $k$ elements are extracted at least once?
In other ...
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1answer
23 views
Uniform sampling of convex polytopes: why is it hard?
There is a surprising number of posts asking about the uniform sampling of convex polytopes (e.g. 1, 2, 3), and an equally surprising number of non-answers (e.g. a, b).
From what I have read, this ...
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1answer
27 views
Proof on how to sample from a truncated exponential distribution
I understand that if i want a sample from an exponential distribution left truncated at a, i can just take a sample from a regular exponential distribution and add the value of a to every single ...
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1answer
113 views
Constructing a probability measure on the Hypercube with given moments
Let $H = [-1, 1]^d$ be the $d$-dimensional hypercube, and let $\mu \in \text{int} H$.
Under these conditions, I can explicitly construct a tractable probability measure $P$, supported on on $H$, ...
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12 views
sampling mechanism for a data pair (X1, X2) where X2 depends on X1
If X2 is dependent on X1, how to generate the random sample of (X1,X2)? One scenario is that we know the prior distribution of X1 and functional relationship between X1 and X2, how to generate the ...
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1answer
17 views
Meaning of “uniformly sampling”?
Reading an article I came across the following expression:
'' $\overline{X}$ is constructed by sampling uniformly along the straight line between the pair of $X$ and $\hat{X}$."
I know what a ...
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1answer
22 views
Probability of having a good set by choosing independently from Universe
Let $S$, $T$ be two disjoint subsets of a universe $U$ such that $|S| = |T| = n$. Suppose we select a random subset $R\subseteq U$ by independently sampling each element of $U$ with probability $p$; ...
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1answer
18 views
Weighted random sample over continuous data
I'm attempting to write an algorithm which gives a random value x in the domain [0-1) and is weighted according to a function. I don't seem to be able to determine how to do this with continuous data, ...
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1answer
13 views
Which shape a sampled point belongs to?
Given a circle and an ellipse, both centered around the origin. The radius of the circle is a, and for the ellipse, the major radius is ...
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0answers
15 views
Distribution of overlapped sampling
Given $n$ i.i.d. random variables $X_i$ for $1 \le i \le n$. Consider a moving block bootstrap sampling with block size $l$: $B_i = (X_i, \ldots, X_{i + l - 1})$ for $1 \le i \le n - l + 1$, there are ...
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1answer
36 views
Sampling subsets of positive numbers with sum close to a given number
Given a set of $N$ positive numbers $a_1 \ldots a_N$, I am trying to generate random subsets of this set such that the sum of numbers in subset is close to a given number $M$.
Suppose I can only ...
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0answers
15 views
Finding the most typical individual in a mutivariate population
I have data for a large number of unique populations. In each population each individual is described by a number of categorical and numeric variables. I want to conduct an analysis on each population,...
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0answers
5 views
How to derive the distribution of mean estimator based on ranked set sampling from normal distribution
I am studying about ranked set sampling from normal distribution.
From wolfe,2004 the joint pdf of RSS is $$f_{1,2,...,n:n}(x_1,x_2,...,x_n)=\prod_{i=1}^nf_{i:n}(x_i)$$
where $$f_{i:n}=\frac{n!}{(i-...
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21 views
How to fill a large Gaussian with N smaller Gaussians
Lets say I have a multivariate Gaussian. I'd like to "pack" that Gaussian full of smaller Gaussians. Intuitively, it seems like I would just sample N points from the original MV Gaussian for the ...
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0answers
31 views
How to sample from a multivariate normal distribution in hyperbolic space?
I want to generate samples from a multivariate normal distribution on the hyperbolic space, such that $\forall x \in \mathbb{H},$
$$ \text{pdf}(x) = \frac{1}{c} e^{-\frac{d^2_{\mathbb{H}}(x,\mu)}{2\...
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1answer
23 views
sampling a connected graph to a smaller connected graph
I have a graph $G$ which has $n$ nodes and $\alpha*(n^2-n)/2$ edges (so the chance of having edge $(i,j)$ is $\alpha$). The graph is connected which means that if we calculate the number of components ...
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25 views
What is the name of this principle?
When generating uniformly-distributed samples from a multidimensional distribution, I believe that sampling each dimension independently produces uniformly-distributed samples from the original ...
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0answers
37 views
Rate of convergence of unknown distribution on an interval
I have an unknown probability distribution $p(x)$. I don't know what it is, but I know it is well-behaved (smooth and normalised and goes fast to 0 at infinity). I've created an illustrated example of ...
