# Questions tagged [beta-distribution]

A two-parameter family of univariate distributions defined on the interval $[0,1]$.

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### Source for KL-divergence of Beta distribution?

This post explains how to derive the Kullback-Leibler divergence between two beta distributions. https://math.stackexchange.com/questions/257821/kullback-liebler-divergence#comment564291_257821 I ...
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### How would we set the initial parameters of beta distribution of Thompson sampling if we want to start the model with the existing data?

This was one of the business-related questions from my technical interview last week for a data science position in a recommender system team at a search engine company focusing on advertisement ...
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### Beta distribution equivalence with two redondant parameters [duplicate]

context In Factor graphs on discrete variables, the parameters are contained in factors associated each with a subset of the random variables in the system. Each factor provides a different positive ...
1 vote
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### How can one confidently choose a p and q for a beta distribution?

Is there a methodology or R tool that allows you to best attribute a p and q value for a Beta distribution? I am currently building a simulation that involves stochastic processes, and from the little ...
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### Is it appropriate to approximate an unknown probability distribution with a beta distribution?

I am creating a model that utilize the output probability distribution of another model, as an input. The model outputs a probability of an event occurring per year, the distribution is a probability ...
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### How to derive the distribution of 1 - X if X is Beta(0.5, 1)

I've been reading about uniform distributions and I'm wondering how statisticians derive these distributions. Lets say we have X, a random variable from the Beta(0.5, 1) density. How could you derive ...
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### How can you calculate the confidence interval for a parameter that's beta distributed when you only have the mean and the standard error? [closed]

i have the mean and the standard error of a parameter that has a beta distribution but unsure how to calculate the 95% confidence interval. Thank you!
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### How to simulate a calibrated prediction model given prevalence and auc

I want to be able to simulate a prediction model given some prevalence of the event and the AUC of the model. I followed the method proposed here but, although this works for giving AUC and predicted ...
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### How to improve the fit of a beta zero-inflated regression model (GAMLSS)?

I'm working with a response variable with values between 0.0 and 1.0. I have a lot of zero. Thus, I'm using beta zero-inflated regression model. Specifically, I'm using the function gamlss from the ...
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### How to prove $Y=X^{2}$ is Beta$\left(0.5,\ 1\right)$ if $X$ is Uniform$(0,\ 1)$

I've been reading about uniform distributions but I can't see how $Y=X^{2}$ is Beta$\left(0.5,\ 1\right)$ if $X$ is Uniform$(0,\ 1)$. Is there a way to prove this using the cumulative distribution ...
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### How to use the exponential distribution to generate samples from the chi-square and beta distributions?

I am supposed to use rexp() in R to draw from an exponential distribution with mean 1, and then use those draws to generate 1000 draws from each of the following: ...
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### Beta distributed transition probability in CEA

I am reading a paper on cost-effective analysis and trying to replicate their results. (paper: https://ascopubs.org/doi/full/10.1200/GO.20.00288) The probabilistic model in the paper assumes that the ...
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### Using Beta Distribution for probabilities over varying time periods

I'm running into an issue with my math not working out as expected and wondering what in my approach is causing it. I'm doing probabilistic analysis using the Beta distribution, with alpha being the &...
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### Prediction of a variable that lies within the interval $[0,1]$ with masses at the ends

I have a data set on kilometers travelled by households and the associated means of transport and now want to predict a means of transport's share in households' total kilometres travelled based on ...
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### How do I write out the components of my beta regression, and how do I interpret them afterwards?

I am estimating a beta-regression using the logit-link function with a continuous dependent variable bound between 0 and 1 and 5 continuous predictor variables. In R the equation is given by: betareg(...
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### Creating a generalized linear model on percent/proportion data that is non-normal, heteroscedastic, and arguably zero-inflated

My objective here is to evaluate how pre-germination treatments (Pre.G) and light treatments (Light) affect percent germination (...
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### What distribution would make a good hyper-prior for a Beta distribution parameterized by mean and sample size?

I have a model which includes a Beta distribution and I am looking for guidance on how to parameterize a hyper-prior for it. For example, this post uses a Beta parameterized with a mean and ...
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### Optimal number of components in a beta mixture model [duplicate]

This is a well-written blog on how we can fit a mixture of beta distributions to a dataset: http://varianceexplained.org/r/mixture-models-baseball/ However, it would have been excellent to identify ...
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### Change shape parameters in a beta distribution based in each datapoint [closed]

I am new to Bayesian statistics and I have been trying to implement a Beta Binomial model from a PhD thesis in rjags. The thesis describes prior distribution for the variables but I am stuck in how to ...
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### Application of spike and slab for sampling from posterior distribution (bernoulli and beta)

I think the gamma N term in the first equation relates to the spike and prior. However, I am unsure what the rhs of the first is used for? Further, I am unsure what the pie term of the second equation ...
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### Inconsistent posterior estimates in Beta-Binomial likelihood vs Binomial in Bayesian, multilevel models?

In this Google Colab, I've simulated Binomial count data and compared the performance of Binomial-likelihood and Beta-Binomial-likelihood models. Both models have the same Beta prior on theta, the ...
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### Beta-Binomial mixture vs Beta-Binomial multilevel model?

I first read about the Beta PDF in the context that it was conjugate to the Binomial distribution; a Beta prior with a Binomial likelihood returns a Beta posterior. So this sounds to me like a ...
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### Finding method of moments estimate for density function $f(x|\alpha) = \frac {\Gamma(2\alpha)} {\Gamma(\alpha)^2}[x(1-x)]^{\alpha - 1}$
Suppose that $X_1, X_2, ..., X_n$ are i.i.d random variables on the interval $[0,1]$ with the density function $$f(x|\alpha) = \frac {\Gamma(2\alpha)} {\Gamma(\alpha)^2}[x(1-x)]^{\alpha - 1}$$ where ...