Questions tagged [sampling-distribution]
The sampling-distribution tag has no usage guidance.
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Distribution of the relative range ($R/\sigma$) [duplicate]
Let us assume a $n$-sized random sample $\{ X_1 , \dots, X_n \}$ from a random variable $X \sim N(\mu, \sigma)$.
Let
$X_\mathrm{min} = \mathrm{min}\{ X_1 , \dots, X_n \}$
$X_\mathrm{max} = \mathrm{...
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Linear Regression - Proof that coefficients estimated via OLS follow a normal distribution [duplicate]
The aim of my question can be better illustrated by this quote extracted from the third chapter of Elements of Statistical Learning (link to book):
I'm trying to understand why, given that the error ...
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Sample covariance of t distribution and degree of freedom
If $X$ is a P by N size matrix, $X_{ij} \sim N(0,\sigma_i^2)$ if I standardize this X matrix with sample mean and sample variance (assuming I don't have access to the population mean and variance) I ...
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Do the 2.5th and 97.5th percentile of the theoretical sampling distribution of a statistic always contain the true population parameter?
I am trying to understand the validity of bootstrap percentile confidence intervals and I have stumbled on the following from these slides:
Suppose we want to set a 95% confidence interval on $θ$, ...
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Proving stability of F1 metric for a given sample size
Okay so say you have sequence classification problem: extracting entities from conversations. Say one of the labels is CITIES.
Say you have calculated P/R/f1/support for CITIES and it looks like this:
...
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Calculating the probability my observation, $Y_i$, is drawn from a random variable $X$?
If I sample a population distribution 2,000 times and get an estimator for the population mean, $\mu$, and the standard deviation, $\sigma$, how can I use these to get the probability that an ...
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Interpretation of distribution that appears when calculating CI for population mean
Let $X \sim \mathcal{N}(\mu, \sigma)$ be the model for a normally distributed population,
described by the probability density function $f_{X}(x; \mu, \sigma)$.
We can denote $\mathbf{X} = (X_1, X_2, \...
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Is it possible that a confidence interval for a sampling distribution of the sample proportion to be < 0 or > 1? [duplicate]
A proportion or percentage must be between 0 and 1, therefore, a confidence interval for a proportion should also be between 0 and 1.
But is it possible that if the "10-successes-and-10-failures&...
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Why use the bootstrap for a skewed statistic when you can use a transform?
Let's say you are working with a statistic (say, the mean of the population) of a skewed distribution with a long, long tail such that confidence intervals must be very skewed to achieve reasonable ...
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Sampling distribution, bias and variance of cross-validation methods (particularly LOOCV)
(TL;DR version below) If my understanding is correct, bias/variance are measures of goodness of fit of a statistical estimator w.r.t. the sampling distribution. So if I have a statistic $t(X)$ that ...
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Bootstrap: Resampling more observations than exist in original dataset
I want to resample an existing study with the primary aim of investigating how the empirical sampling distribution of a statistic varies with different sample sizes.
For example, if the original study ...
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Proper way of constructing sampling distribution
While the proper way of constructing the sampling distribution would be to repeatedly sample from population with unknown parameters, I'm not convinced it is the case in practice. Surveys performed in ...
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Is true that the sampling distribution of $\ln \left(\chi^{2}\right)$ converges to normality much faster than the sampling distribution of $\chi^{2}$?
If true is the consequence true that $X \sim \chi^{2}(k)$ then $\sqrt{2 X}$ is approximately normally distributed with mean $\sqrt{2 k-1}$ and unit variance?
Also true that If $X \sim \chi^{2}(k)$ ...
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sampling distribution of a test statistic when doing permutation test
In a permutation test, we have a test statistic $T$ (for example t-test, f-test, etc.) that is applied to the original data to obtain an observed value $o_{obs}$ for the test statistic. Next, the data ...
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Standard error of sampling distribution mean vs standard deviation of the sampling distribution?
In this resource, towards the bottom, the authors write:
The next step is to estimate the standard error of the mean. If we knew the population variance, we could use the following formula, $sigma_M = ...
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Sampling distribution of GBM Maximum-Likelihood estimator
Given the geometric Brownian diffusion
$$ X_t = \mu X_t \, dt + \sigma X_t \, d W_t$$
I learnt that its maximum likelihood estimators are the following as this web article suggests
$$\hat \mu = \frac{\...
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Calculating the Standard Deviation of the Sampling Distribution when using Bernoulli Sampling
I am trying to calculate the standard deviation of a sampling distribution when using Bernoulli sampling (where each item is given a separate, equal, non-zero probability of being included in the ...
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Is there a good graphical representation for the sampling distribution of relative risk?
For pedagogical reasons, I am interested in communicating graphically the sampling distribution of relative risks (histogram and CDF plot), specifically in the context of a matched-pair study design:
...
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Random samples within the Central Limit Theorem - why select with permutation with repetition?
"The central limit theorem states that if you have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the ...
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Sampling distribution of sample variance
Let $(X_1, X_2, ..., X_n)$ be a random sample from Bernoulli($p$). Find the sampling distribution of $S_n^2=\frac{\sum_{i=1}^n(X_i -\bar X)^2}{n-1}$.
I've just started learning about sampling ...
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Confidence band for simple linear regression - why the curve? [duplicate]
I am really struggling to understand why confidence bands for regression lines have a curve to them. A few example plots showing curved CIs, taken from this post: Shape of confidence interval for ...
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Computing probability distributions over bootstrap samples for two statistics
I have a data set $x= c(0.9575,0.4950,0.1080,0.9359,0.6326)$ and I'm trying to compute the probability distributions for the statistics $\bar X^* - \bar X$ and $\sqrt n(\bar X^* - \bar X)/s^*$, over ...
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Two Sample Z-test with Non - normal distributions (A/B testing)
I am doing my first steps in statistics and your help will be much appreciated. Sorry for not providing any data, since this is just a made-up exercise that I could not quite find the answer for.
Let'...
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Can bootstrapping be used to find the standard error of variance?
I am a bit new to the field and had a question regarding bootstrapping. As bootstrapping gives an idea of the standard deviation of the sampling distribution of the mean, does it also give an idea of ...
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What is the meaning behind a sample distribution if you only have one sample?
I'm trying to understand the meaning behind the central limit theory and the importance of CLT for inferential statistics. The problem that I encountered has to do with sample distributions.
I do ...
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Sampling distribution: sampling with replacement or without?
The following paragraph occurs in Essentials of Statistics for the Behavioral Sciences(10th edition):
If you actually wanted to construct the distribution of sample means,
you would first select a ...
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Binomial vs hypergeometric finite sampling distribution
I was reading these notes:Finite Population Sampling with Application to the Hypergeometric Distribution and I have a question just about the first two pages. The first page, they derive the variance ...
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Estimating population parameter from bootstrapped sample distribution, other than mean value
I'm a rather novice to statistics, so my terminology here might not be totally correct. But I will do my best to explain my question clearly.
My question is about understanding whether it is making ...
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Sampling/Asymptotic Distribution of Estimated Coefficients of Logistic Regression
If I understand correctly, in a logistic regression, we have that $Y_i \mid X \sim Bern(S(X\beta))$ where $S(x)$ is the sigmoid function.
Suppose we estimate $\beta$ using MLE and get $\hat \beta$. ...
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Sampling distribution of Pearson correlation coefficient
Suppose I have draw a random sample of points $(x_i,y_i)$ iid from some distribution, then I compute the Pearson correlation coefficient $\overline{\rho}$ of the points in the sample.
Is $\overline{\...
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Which field of science applies the log-normal sample median distribution?
Which field of science applies the log-normal sample median distribution (i.e. the sample median distribution with samples from a log-normal parent)? I noticed that incubation periods are assumed log-...
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How to use a p-value sampling distribution?
As part of my research I have been looking into the sampling distribution of p-values. Even though p-values are on their way out, they are still used ubiquitously with the normal $\alpha$ =.05 cutoff (...
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How to interpret confidence interval and prediction interval in simple regression "in/with the context of sampling distribution"?
With the context of sampling distribution, in regression analysis, is the following an appropriate interpretation?
Assumptions :
X & Y have a linear relationship
sample size is large enough for ...
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Likelihood function and sampling distribution symbol
I read a introductory stat book that the likelihood function has symbol like , e.g., L(theta, x); while the sampling distribution has the symbol like f(x,theta). May I ask does anyone know whether the ...
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Asymptotic Distribution Using CLT
I have random variables $X_1, X_2, ... , X_n \sim \text{IID } f_X$ using the density function:
$$f_X(x) = \frac{2x}{\theta^2} \cdot \mathbb{I}(0 \leqslant x \leqslant \theta).$$
I have to use the ...
user300224
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degrees of freedom in a t-test in Kruschke's BEST paper
This question is based on a comment by John Kruschke in his BEST paper, pages 589-590.
Kruschke, John K. "Bayesian estimation supersedes the t test." Journal of Experimental Psychology: ...
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Question about the conceptual sampling distribution for one time events
in this paper: Do Political Protests Matter? Evidence from the Tea Party Movement*, the authors use rainfall on the day of the tea party protests as a source of plausibly exogenous variation in rally ...
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right skewed sample does not lead to normally shaped sampling distributions
I will provide R code for a reproducible example. I am calculating the difference in means for two groups. I get a sampling distribution by permutations but instead of a normally shaped distribution ...
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Sampling distribution of the mean of the discrete-power law distribution
For a certain problem I wish to generate random integers $k$ so that their distribution follows $p_k \sim k^{-\alpha}$ for $k \geq k_{\text{min}}$, $k_{\text{min}} > 0$. I am following the ...
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Sampling distribution of the mean of a Beta
Say we have $X \sim \text{Beta}(\alpha, \beta)$. What's the sampling distribution of its sample mean?
In other words, what distribution does the sample mean $\bar{X}$ of a Beta follow?
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Proof that the sampling distribution of the sample variance from $N(0,1)\sim \chi_{n-1}^2$
Is this true? How to verify it?
From the definition of chi square I can not judge whether it is chi square.
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Finding sampling distribution of normal MLE and likelihood
I'm reviewing old exams in preparation for a statistics final, and I'm stuck on a particular question:
Suppose that you have n independent random variables $Y_i$, with each distributed normal with ...
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