Questions tagged [beta-distribution]

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

425 questions
Filter by
Sorted by
Tagged with
16 views

Extended regular variation

In extreme-value theory, an important property of distributions in the Frechet/power-law domain of attraction distribution is "regular variation". My question: What is the corresponding property (if ...
67 views

How reparameterize Beta distribution?

Consider $X \sim N(\mu,\sigma)$; I can reparameterize it by $X = \epsilon\mu + \sigma; \epsilon \sim N(0,I)$ But given Beta distribution $X \sim Beta(\alpha,\beta)$; is there easy way (closed form ...
21 views

Uniqueness of change of variable function

Let $X$ and $Y$ be continuous random variables with probability density function as $p_x(X)$ and $p_y(Y)$. If $X$ and $Y$ are related by an invertible function $f$ as $f(X)=Y$, then using change of ...
35 views

Can adjusted r-squared (or r-squared) be used to compare the strength of independent variables in linear multiple regression?

Relative newbie with quantitative analysis here, so forgive me if the question is naive or ill-specified. I have argued in a manuscript that along with using Beta values in linear multiple regression ...
10 views

truncated predictions for continuous proportion response variable using either beta regression or quasi-likelihood methods

I have tried two approaches for predicting a continuous proportion response variable in both SAS (proc glimmix) and R (glmx): beta regression and a quasi-likelihood approach. I have tried both logit ...
22 views

Issue with proof in Statistical Theory related to Beta and Binomial distributions [duplicate]

Assume $X_n$ is distributed $\text{Beta}(1/n, 1/n)$ and $X$ is distributed as $\text{Binom}(1,1/2)$. Show that $X_n$ converges to $X$ in distribution. I'm having some issue with this question. I ...
16 views

84 views

Bayesian update for Beta distribution

I'm wondering how to find a posterior of a beta distribution when the "new information" is not an outcome of a binomial trial. Let $p$ be the probability of Head of a (biased) coin toss. As usual in ...
43 views

Incoherent post hoc pairwise Tukey test using beta binomial distribution and betareg()

I am fitting a beta binomial regression to my data, which is proportion data (lifetime reproductive success ratio) ranging [0,1]. I transformed the 0s and 1s following Smithson and Verkuilen 2006 (y.(...
51 views

Outlier Detection via Beta Distribution

Suppose I have a continuous random variable which is bound between 0 and 1. The distribution is left skewed like the picture below: My goal is to identify outliers that are small or farther away from ...
19 views

Beta-distribution: how to generate a peak at certain mean value with a control on variance in extrems

Following Distribution that has a range from 0 to 1 and with peak between them?, I generated a beta distribution that has a peak between 0 and 1 at the mean value. When the mean value is 0.5, I can ...
154 views

77 views

Moment Generating Function

Suppose X is a random variable with a Beta distribution and x in (0,1) How can I prove moment generating function exist
41 views

Logistic regression - binary to continuous - how to interpret?

Given data with a binary outcome, i.e.: $0$ = no event, $1$ = event which can be modeled with logistic regression, how then do we understand the following logic: ...
58 views

R package for meta-analysis of beta-distributed data

I am conducting a meta-analysis, and my effect sizes are proportions, with a credible interval for weighing. I think I should assume a beta-distribution, but I do not know which package to use. This ...
62 views

Expectation of Sufficient Statistic for Beta Distribution

I am looking at question 1b of the following notes: http://www.gatsby.ucl.ac.uk/teaching/courses/ml1/asst1.pdf In 1a, I have shown that the Beta distribution has a density that can be written in the ...
21 views

...
118 views

Uber's Pyro less accurate than expected on toy example

Trying to understand the pyro example here: https://pyro.ai/examples/svi_part_i.html which starts with a Beta(10,10) prior, adds 10 Bernoulli likelihood datapoints with a 6,4 split. The analytic ...
217 views

MLE for Beta distribution, with $\beta$ = 3

I'm trying to calculate the Maximum-Likelihood Estimator for $\alpha$, using the beta distribution with $\beta = 3$. I'm kind of stuck at the last bit. Perhaps I've made a mistake somewhere, or this ...
91 views

If $X\sim\text{Beta}(\theta,1)$, obtain the confidence interval of $100(1-\alpha)\%$ based on the asymptotic distribution of the score function

Let $X_{1},X_{2},\ldots,X_{n}$ be a random sample whose distribution is given by $\text{Beta}(\theta,1)$. Obtain the approximate confidence interval of $100(1-\alpha)\%$ based on the asymptotic ...
53 views

Is fair to compare Dirichlet to a Multivariate Beta regression?

I am conducting some analysis on my data I found a strange behavior and would greatly appreciate some guidance or suggestions. I am trying to investigate the effect of a categorical variable (cl) to ...
27 views

Valid highly informative prior for proportion

I am trying to find a prior distribution for a proportion $\theta$ that is highly informative i.e. it is almost point mass at $\theta$ but I am not able to find such distribution that is valid for a ...