Questions tagged [sampling-theory]
For questions related to sampling theory. Sampling theory is the field of statistics that is involved with the collection, analysis and interpretation of data gathered from random samples of a population under study.
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How might one estimate the number of samples in a uniform distribution given only the sample range?
Let's say we have a fair roulette wheel with 2^256 segments, each printed with a unique integer in the range 0 to 2^256 - 1. Let's say that the wheel is hidden from us and that Trevor spins it ...
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Estimating KL Divergence from Multiple Independent Samples
I'm working with two discrete probability distributions, (P) and (Q), and exploring different ways to measure the divergence between them using Kullback-Leibler (KL) divergence. Specifically, I'm ...
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Drawing random samples from statistical distribution
I'm looking for a list of methods to draw random samples from Pareto distributions.
I already found :
Inverse transform sampling
Rejection sampling
Metropolis–Hastings algorithm
Gibbs Sampling
Are ...
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Transformation of random variables to get a sample for another probability density function
Question:
Let $\mathcal{D}$ be a two dimensional unit disk, given by $\mathcal{D}=\{(x,y):x^2+y^2\leq 1\}$. Using rejection sampling algorithm, I managed to generate a two dimensional random vector $(...
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mathmatical formulation for missing information due to sampling
I want to define a mathematical model (formula) to design missing information from sampling. In my problem, I have real events whose value is binary (0, 1) which might change every second. For a given ...
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Efficient Method for Uniform Sampling from the Space of Increasing Vectors in $[0, 1]$
I am seeking advice on methods for uniformly sampling from the space of increasing vectors within the interval $[0, 1]$. Specifically, I require an efficient algorithm that can handle high-dimensional ...
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Relation T-Distribution between chi-square and normal
Theorem. Let $Z\sim N(0,1)$ and $Y\sim \chi^2(v)$ are two independent random variabels. Then, $$T = \frac{Z}{\sqrt{Y/v}} \sim
t-student$$ with degrees of freedom $v$.
Is it the converse always true? ...
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What is the intuition behind the single-pass algorithm (Welford's method) for the corrected sum of squares?
The corrected sum of squares is the sum of squares of the deviations of a set of values about its mean.
$$
S = \sum_{i=1}^k\space\space(x_i - \bar x)^2
$$
We can calculate the mean in a streaming ...
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Why is the demonstration of the "sample" standard deviation somehow more exact than the classic standard deviation, if $\frac{x}{n} ≠ \frac{x}{n-1}$?
I cannot see why to use the "sample standard deviation" instead of the classic "standard deviation" (the "population") ever, most explanations I find are just prescribing ...
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Doubt about sampling without replacement
A problem consists of five numbers $2,3,6,8 and 11$. Consider all possible sample space of size 2 that can be drawn with and without replacement from this population then find
(a) mean of the ...
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Getting my concepts confused with sampling
Let me first set the scene. This is how we learned the variables and their names and symbols.
We have the sugar content of 77 different cereal brands. It firsts asks "estimate the true average ...
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Sufficiency in sampling theory
Introduction
We have a finite population $U$ with $N$ individuals, namely $U:=\{1,\dots,N\}$. Each individual stores a secret fixed value, so let's write $y_i$ for the value corresponding to the $i$-...
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Two boys paradox
I have a question regarding how to form the sample space in this famous paradox.
Usually the sample space is defined as (B,B), (G,B), (B,G) and (G,G). However if I express it as (B1,B2), (G,B) and (G1,...
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An one dimensional sampling version of Penrose tiles in 2D
I was initially interested in aperiodic sampling for signals to address the problem of aliasing in the frequency domain. A design like Penrose tiling in 2D (which is non-repeating) can be very ...
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Sampling a cosine [closed]
If you sample a cosine of fundamental period 0.1 milliseconds with a sampling rate of 10^5 samples per second, how much phase difference is there between two consecutive samples?
I can't solve this ...
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