Questions tagged [sampling-distribution]

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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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1 answer
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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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Using the bootstrap for estimating the odds ratio standard error

I have the following table $$ \begin{matrix} &R = 0 & R = 1 \\ E = 0 &n_{00} &n_{01}\\ E = 1 &n_{10} &n_{11} \end{matrix} $$ If needed, this is census data from a metropolitan ...
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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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1 answer
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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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1 answer
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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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302 views

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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1 vote
2 answers
234 views

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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0 answers
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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 ...
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2 votes
1 answer
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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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5 votes
1 answer
94 views

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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2 answers
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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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3 votes
2 answers
344 views

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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10 votes
2 answers
2k views

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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4 votes
1 answer
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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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3 votes
2 answers
3k views

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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