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54 views

Continuous random sampling with replacement.

Construct a set $s\subseteq[0,1]$ by sampling points in $[0,1]$ with uniform probability density $x\leq1$ so that $|s|=x$. Interpret this as a sampling frame during which data is captured. Now, ...
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229 views

Simulate random sampling with replacement

Any ideas on how to approach this problem? (Due to Karp) Consider a bin containing d balls chosen at random (without replacement) from a collection of n distinct balls. Without being able to see or ...
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1answer
105 views

Monte Carlo Rejection Sampling Method

I have the following passage from a set of lecture notes I am working on that I would like to understand a little better. $\underline{\text{Algorithm for Rejection Sampling}}$: Given two densities ...
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0answers
37 views

Sphere on a grid

So, this is a little tricky kind of a question and I'm not totally sure if it's a mathematic question or a more programming one, but I nevertheless hope to find answers. I want to find out the error ...
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1answer
44 views

variance reduction

Say i have $n$ variables with variances $V_1,V_2,...V_n$. The sum of the variables will have a variance of $V=V_1+V_2+..V_n$ .Now if i am given N total simulations to reduce the variance V, how do i ...
3
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2answers
247 views

Simple random sampling without replacement of huge dataset

For an application I'm working on, I need to sample a small set of values from a very large data set, on the order of few hundred taken from about 60 million(and growing). Usually I use the technique ...
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2answers
919 views

Sampling problem with and without replacement

Find the probability of the event that number $1$ and number $7$ were chosen first and third, respectively at the experiment of choosing five numbers from this set of numbers $\{1,2,3,4,5,6,7,8,9\}$ ...
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1answer
74 views

Sample size requirements in survey

If am doing some market research and want to answer the question "What percentage of the users of a service, searched for the given service online?". Lets say I go out and get people to take a survey. ...
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1answer
953 views

Probability to choose specific item in a “weighted sampling without replacement” experiment

Given $n$ items with weight $w_n$ each -- what is the probability that item $i$ is chosen in a $k$-out-of-$n$ "weighted random sampling without replacement" experiment? Can a closed-form solution that ...
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1answer
66 views

sampling functions and effect on DFT

I'm looking for help on pointing me to the right literature.... My question is as follows... Let's assume I have a discrete function (sinusoidal in nature) sampled at N equi-spaced points. However ...
2
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1answer
480 views

unbiased estimator of sample variance using two samples

I have a couple questions, I'm hoping someone can help! Let $X_1...X_n$ is a random i.i.d. sample from a $N(\mu,\sigma^2)$ distribution, and $Y_1...Y_m$ is a random i.i.d. sample from a ...
2
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3answers
414 views

estimate population percentage within an interval, given a small sample

Given a small sample from a normally-distributed population, how do I calculate the confidence that a specified percentage of the population is within some bounds [A,B]? To make it concrete, if I ...
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1answer
116 views

How to sample from joint Bernoulli distribution?

I have done searches on google.com and here but haven't found a related one. I apologize if this is a re-post. Here is my question: I have a set $n$ of Bernoulli random numbers, and I know the ...
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4answers
359 views

Sampling from a $2$d normal with a given covariance matrix

How would one sample from the $2$-dimensional normal distribution with mean $0$ and covariance matrix $$\begin{bmatrix} a & b\\b & c \end{bmatrix}$$ given the ability to sample from the ...
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1answer
339 views

How to sample from a Gamma distribution with shape not integer

I'm looking for an effective method to sample from a Gamma distribution that has the shape parameter not integer. However, I found everywhere the method to sample from a Gamma with an integer shape ...
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1answer
204 views

Sample-based median calculation

Is there any technique to find the median of a large data set using sampling (or maybe randomized algorithms)?
0
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1answer
72 views

Determining Sample Size - Design Problem

I have a hypothetical problem were say I have a sample size of about 5000 people. I then will collect data on them say, how man calories of food they eat per day for a month. Now I can't obviously run ...
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1answer
38 views

Generating statistics from data samples, that are of snapshots.

My question is part math part computers but I need more of the math answer then a computer answer. I am going to be grabing snapshots of a moment of time on how a computer is performing. Because of ...
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0answers
92 views

Is it possible to calculate/impute the sample size “N” from a given mean and standard deviation?

Can anyone provide with some advice? - thank you I am required to calculate the sample size for two groups, given the following data: Total sample N (group1+group2)=583 group 1: mean=8.35, SD1.07, ...
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0answers
125 views

generating a binomial distribution

I'm trying to sample from a data set using a binomial distribution with parameters p and n. Implementation-wise, I follow these steps I generate an array containing the values of the cumulative ...
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1answer
53 views

Statistics and clarification of Central Limit Theorm

If I have 1,000 participants ranking on a scale of 1 to 10 regarding some object how do I interpret the confidence level and margin of error of the resulting rank? I am used to of seeing 99% ...
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1answer
21 views

What is the name of (1-a)*current + a*sample

Say we take a sample every time unit, we have a calibrated value which needs tracking for drift, however every sample has a given variance causing jumping if we were to use it directly as the new ...
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0answers
151 views

Giving sampling distribution of population total estimator [Homework]

Given sampling data below, Considering a Simple Random Sampling(SRS without replacement) of size 4, what is the sampling distribution of the estimators for total of y's? t1 and t2 where i) t1 is ...
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0answers
69 views

Estimating the number of observations from a set of samples

I repeatedly measure a value $S_n$ which is the sum of a set of $n$ hidden inputs. The goal is to identify the number of hidden inputs. All of the hidden inputs are driven by an experimenter ...
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0answers
40 views

Uniformly sample points over a circular patch of a sphere without rejection [duplicate]

Possible Duplicate: Generate a random direction within a cone A point on a unit sphere $(x,y,z)$ and an maximal angular separation $\theta$ defines a patch with an area of $\Omega = 2 \pi ...
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0answers
100 views

How to sample from a product-of-sums distribution?

$A$ is a $M$x$N$ matrix whose entries are positive. $x$ is a $N$ dimensional binary (i.e. consisting of $0$s and $1$s) vector and the number of $1$s in $x$ is constant. Let $y = Ax$. The distribution ...
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0answers
92 views

Approximability of continuous sampling by discrete sampling - definitions?

Are there standard definitions that express the notion that sampling from a given continuous random variable can be approximated "to any desired degree of accuracy" by sampling from an appropriately ...
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1answer
279 views

uniform sampling of the sphere w.r.t. inner products other than the usual one

I will have a small (usually 2 or 3, probably no bigger than 6) positive integer $n$ and symmetric positive-definite real $n$-by-$n$ matrices $A$, and will want to sample an ...
3
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2answers
185 views

Determining sparse frequency distribution via discrete Fourier transform

Consider the function $$f(t) = 2 \sin(t)+\sin(2t)+25 \sin(400t)$$ (for example). In this case, how many samples of this function would I have to take, and at what sampling frequency, to determine the ...
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2answers
180 views

Sampling a combination randomly

I want to sample a combination of $N$ elements (without replacement) from a list of $M$ elements where $M\gg N$. There are algorithms to do this when each element is picked with uniform probability. I ...
2
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1answer
90 views

$\chi^2$ test and sampling variance

Let $f(x)$ denote the pdf of a $\chi^2$-distribution with $n\in\mathbb{N}$ degrees of freedom given by $$f(x) = \frac{2^{-n/2}}{\Gamma(n/2)}\cdot x^{n/2-1}\cdot\mathrm ...
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0answers
39 views

Sample estimated normal distribution - what will be the expected effect of another sample?

Assume I already have n samples of a 2D variable. I can compute the sample mean and variance. If I assume that the samples are taken from a normal distribution, then using the mean and variance I get ...
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0answers
45 views

How to sample the walk which visits each vertex of a graph specific number of times?

Is there any MCMC mathod that allow me to uniformly sample from all feasible walks where the following restrictions apply: ...
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1answer
17 views

sampling technique: lower error in estimation on using higher sampling rate

I am using sampling to estimate characteristics of a population. My sampling ratio is 32. I take N/32 samples, calculate their sum and multiply by 32. Then I compare it to actual value to get error. ...
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1answer
161 views

Sampling from discrete probability distribution from first principles

I have a set $S=\{a_1,a_2,\dots,a_n\}$. The probability with which each of the element is selected is $\{p_1,p_2,\dots,p_n\}$ respectively (where of course $p_1+p_2+\cdots+p_n=1$). I want to ...
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1answer
118 views

Sampling & Value Prediction and Error Correction?

I am a programmer and I don't have much background in mathematics. I know this question might look much more clear to you if I could articulate it in mathematical terminologies. The problem is this is ...
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1answer
134 views

Sampling $Q$ uniformly where $Q^TQ=I$

(This is related to this question) $Q \in \mathbb{R}^{n\times k}$ is a random matrix where $k<n$ and the columns of $Q$ are orthogonal (i.e. $Q^T Q = I$). To examine $E(QQ^T)$, I conducted monte ...
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1answer
223 views

Hypothesis testing by random sampling

I'm sure this has been asked before, if so please point me to the relevant answers. Anyway, I have about 26000 phone subscription entries in a database. A number of these might contain wrong ...
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1answer
89 views

Adaptive sampling for 2D functions with discontinuities

I have a 2D function, $f(x,y)$, which I can compute on a computer. The function is expensive to calculate, so I would like to use an adaptive sampling method to plot it in a region. That is, I want ...
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1answer
110 views

Designing an efficient sampling strategy

In a Monte Carlo simulation, my goal is to compute an estimate of the mean of a distribution via sampling. Traditional, straightforward statistics generates samples (via simulation) and computes the ...
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1answer
70 views

Should I ignore $0$ when do inverse transform sampling?

Generic method Generate $U \sim \mathrm{Uniform}(0,1)$. Return $F^{-1}(U)$. So, in step 1, $U$ has domain/support as $[0,1]$, so it is possible that $U=0$ or $U=1$, but $F^{-1}(0)=-\infty$. ...
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0answers
45 views

Sampling a distribution with restrictions: eliminating the correlation between two variables

I have a collection of 400.000+ word-pairs. Each word-pair has an association strength, which is a measure of how related the two words are to each other (as in cow-milk). Each word-pair also has a ...
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1answer
95 views

How to statistically sample a map printed on graph paper?

I want to statistically sample a map printed on graph paper by using Google Earth to print out an aerial view of on island to compute the area of the island that is inhabitable by animals. I'm ...
3
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1answer
84 views

Samples in the convex body vs. samples on the convex surface

Let $K$ be a bounded convex body in $\mathbb{R}^n$. Suppose we have a sampler $\mathcal{S}_1$ that can generate points uniformly distributed in $\mathrm{int}K$, and another sampler $\mathcal{S}_2$ ...
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1answer
84 views

Uniform sampling of multicolored balls

If I uniformly sample-without-replacement a small bunch of multicolored balls (say, five colors) from one urn into a "smaller" urn, will the distribution of ball colors in the smaller urn be the same ...
4
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3answers
333 views

What is “sampling from a distribution”?

Exercise 4.11.3 of Grimmett and Stirzaker's Probability and Random Processes reads "Use the rejection method to sample from the gamma density $\Gamma(\lambda,t)$ where $t (\geq 1)$ may not be assumed ...
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2answers
431 views

What is the distribution of gaps?

Randomly select $n$ numbers from the universe $\{1,2\dots,m\}$ with or without replacement, and sort the numbers in ascending order. We can get a list of number $\{a_1,a_2,\dots,a_n\}$, and then we ...
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0answers
45 views

Bias in Resampling

I'm currently doing some work with Particle Filters, a sampling-based method for computing expectations of functions with respect to dynamic (ie: time-variant) random variables. For example, consider ...
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1answer
56 views

Independence of Random samples

I have a some questions that have been bothering for a while now. First, how does one obtain the joint probability distribution function of $X_{1},\cdots ,X_{n}$? Would it be $\prod\limits_{i=1}^n ...
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0answers
432 views

Notation for sampling random variate

Is there standard notation for sampling a value from a probability distribution? Like, if I had a random variable $X$, setting $x$ to whatever value I happened to sample from $X$ on this occasion? I ...