Linked Questions
14 questions linked to/from Beta as distribution of proportions (or as continuous Binomial)
553
votes
15
answers
234k
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 ...
- 9,720
85
votes
5
answers
34k
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 ...
- 1,047
23
votes
5
answers
22k
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 ...
- 395
22
votes
3
answers
12k
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
$...
- 6,232
19
votes
1
answer
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 ...
- 599
22
votes
3
answers
1k
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)^{...
Tim♦
- 130k
8
votes
1
answer
3k
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
2
answers
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 ...
- 1,241
2
votes
3
answers
295
views
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 ...
- 201
5
votes
1
answer
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 ...
- 123
1
vote
3
answers
1k
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 $\...
- 281
2
votes
1
answer
299
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 ...
- 1,024
1
vote
1
answer
106
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 ...
- 247
1
vote
1
answer
201
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 ...
- 11