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### 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 ...
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### 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 ...
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### 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 ...
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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 $... 1answer 2k views ### Antonym of variance Is there a word that means the 'inverse of variance'? That is, if$X$has high variance, then$X$has low$\dots$? Not interested in a near antonym (like 'agreement' or 'similarity') but specifically ... 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)^{... 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 ... 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 ... 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 ... 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 ... 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$\...
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 ...