# Questions tagged [beta-distribution]

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

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20 views

### Correct distribution to model proportion of time in a day

I would like to determine how the presence of researchers influenced the amount of time that shorebirds spent on the nest in a day. My data consists of proportions that range from 0.715-0.997, which ...
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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 ...
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### dbeta vs dbinom output comparison [duplicate]

My understanding of how density functions work in R is that they are calculations of the absolute probability (continuous) or probability mass (discrete) of something occurring, instead of the ...
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### Beta Binomial Distribution Derivation- Bayesian

This is from Hoff's Book:First Course in Bayesian Statistics How is p(y|θ) in equation (1) is similar or different than that of equation (2)?. In equation (1) p(y|θ) is treated as joint ...
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### Beta-Binomial conjugate proof

Can someone explain this proof to me? I get stuck on the transition from the third line to the last line. Namely: Is the integral being evaluated or not? How does the entire expression reduce to a ...
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### Bayesian priors and probability distributions

Book "Bayesian Statistics the Fun Way: Understanding Statistics and Probability with Star Wars, Lego, and Rubber Ducks", chapter 9 "Bayesian priors and working with probability ...
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### Analytical power analysis of a binomial RCT

I have a certain population of users of my free app, with new ones installing every day. I want to run an RCT on them, specifically measuring the impact of some change on their conversion rate (i.e. ...
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### Beta distribution meaning? [duplicate]

I am trying to understand what is the meaning of Beta distribution. I can try compare it to classical probability of event that when I throw the dice it will be let's say 1, that is 1/6. Btw also try ...
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### Analyzing data that appears to be drawn from a beta distribution

I have proportional data where each of 10 "trials" (actually plant seeds) occur per sample. The 10 trials per sample are not independent, so if one fails (is eaten), the others are likely to fail. On ...
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### Why marginal impact of an observation to the posterior decreases in Bayesian inference?

When we toss a coin with an unknown Heads probability $p$, we can use Bayesian inference to estimate the unknown value $p$. Say, we start with a Beta prior distribution with parameters $(a,b)$ and ...
416 views

### Why does the proportion of native language speakers have an arcsine like distribution?

Based on actual data, given below is the distribution of the languages spoken in India by nearly $1.4$ billion people. There are more than $1600$ active languages in India which have been classified ...
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### DHARMa diagnostics show significant deviations in KS tests for a glmm with beta distribution

I'm trying to use glmmTMB to fit a beta-distributed generalized mixed effects model with nested random effects. DHARMa residual diagnostics show a KS test with significant deviation. Is this serious ...
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### Incomplete beta function increasing in $\alpha$

Let $I_{x}(\alpha,\beta)$ is the regularized incomplete $\beta$ function, aka the cdf for a random variable with distribution $\text{Beta}(\alpha,\beta)$. In a recent paper (https://arxiv.org/abs/...
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### Can we compare the beta for one predictor across two nested linear mixed-effect (LME) models or generalized linear mixed-effect models?

In my experimental linguistics research, I would like to evaluate how an interaction effect is influenced by additional predictors. To be precise, suppose there are 10 questions in my experiment. The ...
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### Using PDFs to calculate optimally weighted average

I want to calculate the expected value of a parent node in a search tree, where the parent node has three children A, B, C. The goal is that the expected value of the parent should reflect the ...
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### Parameters of beta distribution with a given HDI [duplicate]

Is there some way to calculate the parameters of a beta distribution, if the highest density interval is known. That is, given $a,b,x$ I want to have a beta distribution such that the probability of ...
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### Bayesian Estimation, What is Equivalent Sample Size or Imaginary Sample Size?

I am trying to understand the formula given in the book Bayesian Networks, With Examples in R, by Marco Scutari & Jean-Baptiste Denis. The formula estimates the parameters of a categorical ...
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### How to choose the appropiate beta regression model type and variables?

Recently, I got my hands on modelling proportions [0,1]. Due to data type many of my variables are 0 and 1 inflated. Some of them are delicately affected by the bound values and some are heavily. I ...
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### Deriving variance of Beta distribution using $E[Z^m(1-Z)^n]$

I have been kind of stuck on this exercise for quite a bit: I can compute the integral and set the parameters to get the mean. Now for the variance, I have a feeling there must be some easy way to ...
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### Is a multivariate Beta Regression appropriate for modelling multiple dependent variables where each variable is a percentage?

I have a dataset with multiple predictors, some discrete and some percentages. My response variable is essentially 3 categories: percentage of high, medium and low life satisfaction, or maybe they are ...
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### Clarification on Bayesian hypothesis testing

I understand the mathematics behind Bayesian hypothesis testing, however I'm struggling to find many examples, specifically ones that apply to the problem I'm working on and was hoping to get some ...
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### How to report results for generalised linear mixed model (glmmTMB) with beta distribution and logit link?

I am currently analysing the effect of canopy cover on the proportion of birds scavenging on carrion left out in nature. The data comes from several national parks, which I included as a random factor....
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### Joint Distribution of Two Independent Variables Beta distribution

I am a newbie when it comes to STATS (regretting taking this course..). I need help with this homework question I have. I have gotten two density distributions using ...
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### Integrating beta distribution for hypothesis test [duplicate]

Given we are testing $H_1: \pi > 0.5$ where $\pi \sim \beta_{(35,24)}$ and $a =0.1$, the direct calculation is, $P(\pi \leq 0.5) = \int_0^{0.5}\frac{1}{B(35,24)} x^{34}(1-x)^{23}\;\mathrm{d}x$. ...
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### Am I statistically allowed to use a binomial family here -> is my data truly independent?

I'm having trouble with finding the most suitable analysis for my data. I'm investigating the behaviour of wild animals in nature. More specifically, I'm looking at animals scavenging from carcasses ...
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### Regression alternatives for proportional data that do not rely on the 0 - 1 interval

I'm currently analyzing data consisting of change in cognitive performance and how it is related with a physiological variable (enzymatic activity) in a group of people. As all people were assessed ...
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### Proving independence relationship

Let $X_1,X_2,X_3$ be continuous positive random variables satisfying $X_1+X_2+X_3<1$ and the following independence relations $$\frac{X_1}{X_1+X_2}\perp \!\!\!\perp \frac{X_3}{1-X_1-X_2}~ and$$ \...
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### Choosing a ‘noninformative’ hyperprior distribution

I am trying to better understand hierarchical Bayesian models. I started here: https://blog.dominodatalab.com/ab-testing-with-hierarchical-models-in-python/ And ran into the following sentence ...
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### How can I understand if my Beta Distribution is converging?

I am evaluating a Bayes AB Test on 2 variants, A and B. I then plotted a graph which shows the Probability of B is better than A on a daily basis. My worry comes in on the topic of 'peeking'. Let's ...
To get the number of "positive cases" I'm in doubt between two strategies. The first one is to draw samples from a Beta distribution: $p \sim Beta(\alpha + cases, \beta + non\ cases)$, using these ...