Questions tagged [beta-distribution]

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

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Sampling from multivariate Bernoulli

Suppose you have a vector p drawn from a multivariate Beta distribution (not a Dirichlet), such as the one described here ( How to construct a multivariate Beta distribution? ) with a Gaussian copula. ...
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Comparing models with the betareg packpage

I'm having problems using betareg. I have a dataset that always shows different results depending on how I perform the analysis. I'm using ...
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Does log-rank statistic converge in distribution to a beta distribution or Pearson I distribution?

The logrank test statistic compares estimates of the hazard functions of the two groups at each observed event time. It is constructed by computing the observed and expected number of events in one of ...
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Probability density function of a zero-inflated (or zero-one-inflated) beta distribution?

I am interested in plotting the PDF of a zero-one-inflated beta distribution so that I can overlay an empirical density function of the observed data, with a PDF using the parameters I estimated from ...
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Distribution of the ratio of dependent non-central chi-square random variables

I am working on a problem that is similar to the one discussed in this link. But in my case $X_i \sim \mathcal{N}(1, \sigma^2)$, i.e., $X_i$ is not a zero-mean Gaussian RV. Specifically, I want to ...
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Calculate grouped mean/quantiles when sample size not known

First off, I should say that I come from a clinical background and haven't taken any formal stats courses (realising it's high time I did that!), so apologies if this question seems quite basic. I'm ...
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Beta distribution Bimodal?

The Wikipedia site for Multimodal Distributions states "Important bimodal distributions include the arcsine distribution and the beta distribution". I thought the beta distribution is ...
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Interpreting the quantities sampled from a Dirichlet distribution

Suppose you sample $M$ vectors from $Dirichlet_K(\alpha)$. You then show a histogram summarizing the distribution of the $M$ values that were sampled for dimension $k = 1$ (i.e. the first dimension, ...
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References for the conjugate prior to the beta distribution?

The Wikipedia article about "Conjugate Prior" has a table containing information about Likelihood Distributions with their Conjugate Priors. In the "Continuous Likelihood" table, ...
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Intuition behind Beta Distribution's degrees of freedom

I believe this is a duplicate of this post, but I think someone can easily clarify my misunderstanding of the Beta pdf: $f(x)=\frac{\Gamma(a+b)}{\Gamma(a)\Gamma(b)}(x)^{a-1}(1-x)^{b-1}$ for $x\in[0,1]$...
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Modeling the precision and location parameters in beta regression

Is there any technical or substantive reason to typically want to ensure the location $\mu$ and precision $\phi$ parameters in the beta regression model include the same fixed or varying predictors?
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How do find the best arm in a multi-armed bandit when exploitation is unimportant?

I have a problem similar to the 'Bernoulli bandit' problem in the exploration-exploitation paradigm, but without the exploitation element. In particular, I have many levers that I can pull and each ...
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Beta regression (proportions) with phylogenetic comparative analysis?

Is there a package in R that allows phylogenetic comparative analysis of proportion data (i.e. a beta distribution)?
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Mathematical Definition of Parameters

I am currently trying to differentiate the parameters in the beta generalized Gompertz distribution by Benkhelifa which has the following CDF and the following PDF with all parameters being larger ...
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Finding probability of occurrence in non-standard distributions

I'm writing a program that uses standard deviation as a threshold to detect outliers, however I understand that this assumes a normal distribution, however the data I'm using can assume any ...
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Using conjugate priors to estimate the posterior distribution of a proportion of a region composed by subregions

Let's say I have a region that is divided into 3 subregions. In each subregion, I run ~90-110 randomly allocated surveys asking a binary question. I want to know if the way that I am estimating the ...
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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 ...
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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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Bayesian Test in hypothesis testing with Bernoulli random variables

Let $X_1,\ldots , X_n$ be iid Bernoulli$(p)$ $(0<p<1)$. Our sample is $x_1=\ldots x_n=1$. Suppose that the prior distribution of $p$ is Uniform$(0,1)$. Consider a Bayesian test for $H_0: p\geq 0....
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Beta coefficient related to percent change?

I am trying to determine the factors that impact changes in bat activity across the midwest. I am using package MuMIn to rank the following factors: habitat, park, years since white-nose syndrome ...
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Mixed Model with beta response and glmmTMB

I conducted an experiment in which I am trying to model the relationship between my response weed_coverage [%] and the predictors soil moisture [%] + treatment + distance. Weed_coverage and ...
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Can I use a Prior with Simulated data?

I have a prior about some proportion that follows a Beta distribution. Unfortunately, I do not have (yet) observed data but I was offered a thousand simulated datasets. Each dataset comes from ...
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Can beta regression be used with continuous numerical data?

I am trying to fit a generalized linear model with Gamma distribution in R, but when I examine the residuals they are not normally distributed. I have a continuous numerical response variable, ...
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Histogram of the MLE of the probability in binomial distribution and the plot of beta distributions

I have data with columns "y" and "n", which for this example can be "y" count of heads out of "n" coin flips. There are "i" rows ie "i" ...
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How to derive the distribution of 1 - X [duplicate]

Suppose X is a random variable from the Beta(0.5, 1) density. I want to derive the distribution of Y = 1 − X My attempt: $F_{1-X}(\alpha)= P(1-X \leq \alpha) = P(1-\alpha \leq X) = P(X\geq 1-\alpha) =...
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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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Replace parameter with estimate for confidence interval. Case Beta distribution

I'm trying to get a confidence interval for the mean of a beta distribution $B(\theta,1)$, using $[\hat\theta - z_{1-\alpha/2}\hat\sigma_{\hat\theta};\hat\theta + z_{1-\alpha/2}\hat\sigma_{\hat\theta}]...
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Simulating Correlated Continuous Variable Given 2 Existing Binary Variables

I am looking to draw samples from a Beta distribution (let's say α = 3 and β = 2) conditional on two existing binary variables in a correlated manner. Let's call the variable distributed as a Beta as <...
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Is there a "beta distribution" over the entire real line?

The malleability of the beta distribution pleases me; it can be symmetric, asymmetric, platykurtic and so on, as the following picture shows us: I thought it would be interesting to use it to model ...
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Distribution of the exponential of an exponentially distributed random variable?

Let $X$ be an exponentially distributed random variable, that is, with density function $f(x)=\lambda e^{-\lambda x}$ for $x\ge 0$ ($\lambda>0$), and cdf $F_X(x)=1 - e^{-\lambda x}$. What is the ...
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Expectance of predictive posterior on binomial-beta modeling

I'm struggle with figuring out how to prove: $E(\tilde{x}|x)=n\frac{a1}{a1+b1}$ where $x|\theta \sim Bin(n,\theta)$, $\theta \sim Beta(\alpha,\beta)$ and so $\theta|x\sim Beta(a_1=\sum{x_i}+\alpha,a_2=...
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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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