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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23 views

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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29 views

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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1answer
26 views

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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1answer
51 views

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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9 views

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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1answer
30 views

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 ...
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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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1answer
92 views

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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46 views

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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1answer
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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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1answer
41 views

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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1answer
32 views

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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How do I calculate the parameters of the beta distribution from the mean and the variance? [duplicate]

My mean is 10 and the variance is 4. There has been confusion around the bounds of $\mu$ and $\sigma_2$ for any given Beta distribution, what I understand is, $$ \mu = \dfrac{\alpha}{\alpha + \beta} ...
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Realization of a Beta distribution function from a derived Exponential function

So we have a beta distribution Y∼Beta(1,β) and a random variable X which is given by the equation X=−log(Y) I found the cumulative distribution function of Y to be Then I found the cdf of X So X is ...
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Bayesian Analysis: Point Estimates for a Beta Posterior

I think this is a fairly beginner bayesian analysis question. I have a Beta Posterior with $\alpha = .32$ and $\beta = 1.35$ (estimated using MCMC), that describes a probability. My question is: ...
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Can this statistic be shown not to be sufficient for $\theta$?

This problem comes from Casella and Berger, who do not rigorously demonstrate (in their solution key) that the statistic is not sufficient. Let $X_1,\dots,X_n$ be a random sample from a population ...
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Why are $\mathbb{E}( \ln(x))$ and $\mathbb{E} ( \ln(1 - x))$ reasonable descriptions of knowledge about a beta distribution?

The max entropy philosophy states that given some constraints on the prior, we should choose the prior that is maximum entropy subject to those constraints. I know that the Beta($\alpha, \beta$) is ...
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1answer
537 views

Why is the Beta Distribution Called the Beta Distribution?

In my research, I've been unable to find a historical explanation for why the Beta distribution has the name it does. I'm aware of what Wikipedia says about how it got its name, but so far I haven't ...
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Why are beta distributions commonly chosen for priors? [duplicate]

Is there any specific reason why a Beta distribution would be chosen as a prior, other than that it is conjugate for the Binomial?
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Estimating Beta distribution parameter from Pert distribution ones

The Pert distribution is a modification of a Beta distribution defined by 3 parameters (a, b, c). Is it possible to specify the underlying Beta from those 3 parameters, transforming them into the ...
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Transformation of Beta distribution prior parameters for group testing analysis

As described here Optimization of pool size and number of tests for prevalence estimation via group testing I'm trying to estimate the prevalence of a lab test in a population (PCR for COVID-19) ...
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1answer
79 views

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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Argmax of betas

Let $\theta_i \sim \text{Beta}(\alpha_i, \beta_i)$ for $i \in I$. What is the distribution of $i^\ast = \operatorname*{argmax}_{i \in I} \theta_i$? Let $[X]$ denote the CDF of a random variable $X$. ...
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1answer
84 views

is this a decent model fit?

I am new to linear modeling (first time using glmm, brms, etc). I am just wondering if the family and formula I am using are decent for my data. I am running a beta distribution for my percentage data....
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1answer
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Relationship between Binomial distribution and the Beta distribution [duplicate]

I have been investigating the details of the Beta distribution and the Binomial distribution and have 2 questions to ask, but first a slight preamble to explain the background to my questions. In the ...
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1answer
60 views

Confused about over dispersion for my beta distribution

I have percentage data so I am using a beta distribution and I want to do a mixed-effect model so I am still trying to decide between glmmTMD or the brm packages. I saw somewhere that some ...
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1answer
83 views

How to generate random data, that's from Beta distribution with specific density function in R?

So, considering that $\theta = 2$ and density function is $f(x) = \theta x^{\theta - 1}, 0<x<1$ and $0$ anywhere else, how do I generate random data from this particular distribution? Here is ...
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cant seem to do random slope intercept model because I am missing values, any way around it?

I have a data set with 3 fixed effects categories region(2 levels), genus(2 levels), and food(5 levels). I am looking to see if sponges have different retention efficiency of the different food type ...
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1answer
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Trying to determine which distribution to use for my percentage data for mixed effects model

I am seeing a lot of different answers to percentage data, either beta or binomial with a logit link and not to use poison distribution because it isn't count data. My response variable is retention ...
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1answer
26 views

I need to construct function that gives out data of specific pdf function and draw histogram of it [closed]

So, the given density function is: $\theta x ^{\theta - 1}, \ \ if \ \ 0<x<1 \text{ and } 0 \ \ \text{ otherwise}$. $\theta$ is given as 2. I also need to draw a line that corresponds the ...
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How to generate numbers from Beta distribution in R if one of the parameters is $\theta$?

I have to estimate ( using method of moments) $\theta$ with an estimator $\hat{\theta}$ for a function with pdf given as $$\theta x^{\theta-1}, \ \ \ \text{ for 0 < x < 1, and } 0 \ \text{ ...
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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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1answer
39 views

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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55 views

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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1answer
44 views

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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23 views

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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82 views

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 ...
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29 views

Gamma to Beta: Successes and Failure Proportions?

I have a question after reading this article on the relation between Gamma and Beta distributions and this article on the intuitive understanding of the Beta Distribution. Question As the Gamma ...
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1answer
126 views

A beta distribution multiplied by a constant and a binomial distribution based on it are equal?

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 ...

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