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: ...
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1 answer
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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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2 answers
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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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1 answer
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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 ...
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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 ...
15 votes
1 answer
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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 ...
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1 answer
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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, ...
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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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1 answer
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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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1 answer
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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 ...
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647 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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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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1 answer
426 views

Beta-Binomial parameter estimation

The MLE or method of moments estimation of parameters of a beta-binomial distribution makes use of (c, y) -- total number and positive counts. However, if we only have one such pair, then $\frac{\...
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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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How to estimate beta distribution parameters using a beta binomial with empirical bayes

I would like to estimate parameters for a beta distribution using a maximum likelihood approach in python (as mentioned here). I can do this for a beta: ...
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1 answer
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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 ...
2 votes
1 answer
244 views

How to calculate confidence intervals for a generic (non-normal) pdf

In particular, this is a question about distributions with some skew and/or where the mean, median and mode might all be different. For any pdf, it's possible to find multiple different domains within ...
12 votes
2 answers
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Scaling the backward variable in HMM Baum-Welch

I am just trying to implement the scaled Baum-Welch algorithm and I have run into a problem where my backward variables, after scaling, are over the value of 1. Is this normal? After all, ...
9 votes
1 answer
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Product of beta distributions

I am looking at trigger efficiencies, meaning that I have some device that fires on $k$ out of $n$ events. In the end I am interested in some estimate of the efficiency $\epsilon$ which is 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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1 answer
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How to fit newer cohorts using Pareto/NBD or Beta/Geo for CLTV

I am trying to fit the popular Pareto/NBD or Beta/Geometric models for non-contractual, continuous customer data. On top of that I then fit the Gamma/Gamma model for monetary value (using the very ...
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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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Bayesian A/B/C testing

I built a Bayesian A/B testing tool - i.e. one which models A and B having posteriors $Beta(\alpha_i, \beta_i)$ where $\alpha_i, \beta_i$ are updated every iteration. After T iterations, I compare ...
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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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1 answer
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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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1 answer
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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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15 votes
5 answers
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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3 answers
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How to convert the parameters in a binomial distribution to those in a beta distribution?

I know that the beta distribution is the generalized continuous case of the discrete binomial distribution. Let's say I have a binomial distribution, $B(N,p)$. I would like to know the corresponding $\...
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2 answers
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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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1 answer
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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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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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2 answers
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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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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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2 answers
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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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1 answer
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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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