# Questions tagged [beta-distribution]

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

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### Expected Beta distribution within a group

I have a group a baseball players and I have to calculate the expected beta distribution of each player. Groups Group 1: Hits: 30, Misses: 471 -> $Beta_1(30, 471)$ = a/(a+b) = 5.99% Group 2: Hits: ...
1 vote
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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. ...
1 vote
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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 ...
1 vote
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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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### 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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### 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 ...
23 views

### 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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### Distribution of the ratio of dependent chi-square random variables

Assume that $X = X_1 + X_2+\cdots+ X_n$ where $X_i \sim N(0,\sigma^2)$ are independent. My question is, what distribution does $$Z = \frac{X^2}{X_1^2 + X_2^2 + \cdots + X_n^2}$$ follow? I know ...
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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 ...
1 vote
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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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### How to construct a multivariate Beta distribution?

What is a multidimensional generalization of the Beta distribution, in compliance with the following specification? I am not looking for the Dirichlet distribution. I am looking for a generalization ...
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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, ...
1 vote
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### Inferential statistics for vector of percentages

I'm getting confused by this and was wondering if someone can enlighten me: I have a random sample consisting of 50 percentages. Each percentage can take on any value between 0% and 100% inclusive ...
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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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### 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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### What is the likelihood function of this random variable (beta distribution parameterizing a Bernoulli distribution)?

This is related to an earlier self-study question of mine. The setup is that there are $N$ individuals, indexed by $i$, and two time periods. Individuals choose whether to "invent" something in the ...
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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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### floc and fscale in fitting Beta distribution in Scipy — getting FitSolverError

I have a dictionary with unique ID and a list of floats as key/value pairs, e.g.: '101':[0.6, 0.8, 0.3, 1.0, 0.0, 0.0, 0.41, 0.34, 0.54]. Each list of floats has at least 9 values long and always ...
1 vote
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### Why does my Cullen and Frey Plot indicate a Beta distribution even though it is not a probability distribution?

I am trying to build a model that will estimate people's willingness to pay for a certain good. My dataset is comprised of more than 1000 observations and 30 variables. This is how my 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 ...
1 vote
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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 ... 8k views

### How can I (numerically) approximate values for a beta distribution with large alpha & beta

Is there a numerically stable way to calculate values of a beta distribution for large integer alpha, beta (e.g. alpha,beta > 1000000)? Actually, I only need a 99% confidence interval around the mode,...
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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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### rate of convergence acceptance-rejection vs inverse transform sampling

Does the acceptance-rejection method or inverse transform sampling converge to the mean quicker say for beta distribution, assuming acceptance-rejection has suitable envelope function? is there a way ...
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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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