Linked Questions

553 votes
15 answers

What is the intuition behind beta distribution?

Disclaimer: I'm not a statistician but a software engineer. Most of my knowledge in statistics comes from self-education, thus I still have many gaps in understanding concepts that may seem trivial ...
ffriend's user avatar
  • 9,720
85 votes
5 answers

Central limit theorem for sample medians

If I calculate the median of a sufficiently large number of observations drawn from the same distribution, does the central limit theorem state that the distribution of medians will approximate a ...
user1728853's user avatar
  • 1,047
23 votes
5 answers

Distribution that has a range from 0 to 1 and with peak between them?

Is there a distribution or can I work from another distribution to create a distribution like that in the image below (apologies for the bad drawings)? where I give a number (0.2, 0.5 and 0.9 in the ...
Stan Callewaert's user avatar
22 votes
3 answers

What is the relationship between the Beta distribution and the logistic regression model?

My question is: What is the mathematical relationship between the Beta distribution and the coefficients of the logistic regression model? To illustrate: the logistic (sigmoid) function is given by $...
tomka's user avatar
  • 6,232
19 votes
1 answer

Antonym of variance

Is there a word that means the 'inverse of variance'? That is, if $X$ has high variance, then $X$ has low $\dots$? Not interested in a near antonym (like 'agreement' or 'similarity') but specifically ...
Hugh's user avatar
  • 599
22 votes
3 answers

Why is there -1 in beta distribution density function?

Beta distribution appears under two parametrizations (or here) $$ f(x) \propto x^{\alpha} (1-x)^{\beta} \tag{1} $$ or the one that seems to be used more commonly $$ f(x) \propto x^{\alpha-1} (1-x)^{...
Tim's user avatar
  • 130k
8 votes
1 answer

Taking into account the uncertainty of p when estimating the mean of a binomial distribution

I have a binomial distribution with parameters $N$ and $p$, and the estimate for the mean of my distribution is N$\times p$. The values of $N$ and $p$ are such that we can use the Gaussian ...
Helga Holmestad's user avatar
7 votes
2 answers

Weighted arithmetic mean weight choice in a simplified Bayes estimator

A Bayesian estimator as defined in the Wikipedia article Practical example of Bayes estimators balances the prior knowledge of the entire data set with the knowledge of the subset. This is usually ...
Chris's user avatar
  • 1,241
2 votes
3 answers

We're estimating mean, variance, proportion or compare samples with them. I understand for mean and variance. But why is it required for proportions?

I have learned how to estimate a mean, variance or proportion from a sample. and also, how to compare those for samples. I'm understanding well why we might need to estimate or compare means or ...
Marc Le Bihan's user avatar
5 votes
1 answer

Conjugate beta / interpretation of the "continuous binomial" signal

Note: this question has significantly evolved, thanks to inspiring comments by Tim. Assume there is some "truth" $x\in[0,1]=Beta(1,1)$ that is signaled with some precision. I assume that the ...
Joanna F's user avatar
  • 123
1 vote
3 answers

How to convert the parameters in a binomial distribution to those in a beta distribution?

I know that the beta distribution is the generalized continuous case of the discrete binomial distribution. Let's say I have a binomial distribution, $B(N,p)$. I would like to know the corresponding $\...
Matthew Hui's user avatar
2 votes
1 answer

Bias in beta regression

I just wanted to check how good my Beta reg model was at recovering true values of the parameters, and I found surprisingly large differences. Same results when using the "betareg" package. Here is ...
Nicolas K's user avatar
  • 1,024
1 vote
1 answer

Putting a prior distribution on average GPA

I am trying to see what would be an appropriate prior distribution for $\theta$, the average GPA of all college students who graduate in a particular year Y from university U. Assume also that from ...
Orest Xherija's user avatar
1 vote
1 answer

Determination of sample size for a proportion

SCENARIO The parent company has other business units (think of these as franchises owned by the parent company). In order to quality assure procedures the parent company samples employees’ work at ...
Log On's user avatar
  • 11