Linked Questions

520
votes
15answers
213k views

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 ...
72
votes
5answers
26k views

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 ...
18
votes
5answers
13k views

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 ...
19
votes
3answers
9k views

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 $...
19
votes
1answer
2k views

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 ...
19
votes
3answers
925 views

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)^{...
7
votes
1answer
2k views

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 ...
7
votes
2answers
2k views

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 ...
5
votes
1answer
1k views

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 ...
1
vote
1answer
232 views

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 ...
0
votes
2answers
466 views

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 $\...
1
vote
1answer
178 views

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 ...
0
votes
1answer
76 views

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 ...