Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [sampling-distribution]

26 questions
10
votes
2 answers

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?
Josh
  • 3,408
  • 4
  • 22
  • 46
6
votes
3 answers

Confidence band for simple linear regression - why the curve?

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 predicted values in linear regression I have read a…
dataphile
  • 63
  • 3
5
votes
1 answer

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 attendance, i.e. an as an instrumental…
Steve
  • 385
  • 3
  • 10
4
votes
1 answer

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.
Richard Lin
  • 81
  • 1
  • 4
3
votes
1 answer

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 distributions of statistics. I have found out that…
Tapi
  • 133
  • 5
3
votes
2 answers

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 procedure given in this review (page 699). Now the problem…
Peaceful
  • 603
  • 3
  • 19
3
votes
2 answers

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 expected value $\beta x_i$ and known variance…
Florian D'Souza
  • 175
  • 2
  • 9
2
votes
1 answer

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's assume we have two separate datasets and each…
vvan
  • 23
  • 4
2
votes
0 answers

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 $\hat \beta$. Now, from what I found online, $\hat\beta$ doesn't…
Dayne
  • 2,113
  • 1
  • 7
  • 24
2
votes
1 answer

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: General 142.2 (2013): 573. Consider...a case in which there is…
Dave
  • 28,473
  • 4
  • 52
  • 104
2
votes
2 answers

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 centered at 0 I am getting this. Can someone…
tomas hujo
  • 21
  • 2
1
vote
1 answer

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 all bootstrap samples of size 5 (the same size as…
Novice
  • 531
  • 2
  • 9
1
vote
2 answers

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 random sample of a specific size (n) from…
Mainul Islam
  • 127
  • 5
1
vote
1 answer

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 and expected value of the mean, or sample…
Steve
  • 385
  • 3
  • 10
1
vote
1 answer

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 sense to use bootstrapping method to calculate a…
Bicycle-riding Dog
  • 13
  • 3
1
2