Questions tagged [beta-distribution]

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

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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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Sum of elements in a Dirichlet random vector conditional on one element is greater than another

I'm working on a research project in machine learning but I was stuck at some point while developing a theory background of the project. Let $(X_1,X_2,X_3,X_4)\sim Dir(\alpha_1,\alpha_2,\alpha_3,\...
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Tail bound of beta distribution when $\alpha$ is sufficiently close to zero while $\beta$ greater than 1

I am interested in finding sharp enough bound for tail probability $\Pr(X\gt t)$ given $X\sim \operatorname{Beta}(a,b)$ when $a$ is very close to 0 while $b$ is fixed value greater than 1. Numeric ...
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Fitting a Beta distribution only using coin flips from the biased coins it generates

I have a Beta distribution $D$ with unknown parameters $\alpha$ and $\beta$ which I wish to estimate. If I was given samples $p_1, \ldots, p_n$ from $D$, then it's relatively straightforward to fit $...
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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 ...
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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.(...
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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 ...
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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 ...
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Is $f(t,\beta ,\mu , \theta )= e^{\theta(t-\mu)^{\beta}}$ a well known distribution on the unit interval?

$\newcommand{\erf}{\operatorname{erf}}$ I have tried out to define a new distribution lie in [0,1] using my special function which is montioned in this paper, The new special function is defined as: $...
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Are the beta distribution and binomial distribution related? [closed]

I've seen questions like this and this, but it hasn't quite answered my question. How intertwined are the Beta and Binomial distributions? A quick sidenote: the Poisson distribution and the ...
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Can I plot a beta distributed model with percentage rather than proportion? [closed]

I am analyzing a response variable (herbivory) which is a proportion, so I am using betareg function from the betareg package. The structure is similar to the GasolineYield dataset, so using it as ...
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Geometric distribution with a capped number of trials - finding expectation and prior predictive distribution

So I am modeling a random variable which follows a geometric distribution with probability $\theta$ except that the total number of trials is capped at some value $n$. I.e., the probability mass ...
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How do I use a beta distribution to model this bimodal data?

I am trying to model data that looks like this: The data reflects frequencies of items at 0, 25, 50, 75, and 100. The majority of the time, values are concentrated at the 0, and 100 points. I believe ...
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Deriving conditional probability of bivariate bernoulli by using Dirichlet

While I was working on my research project, I found it difficult to derive a conditional probability from Dirichlet dist. Consider two Bernoulli trials that are possibly correlated with each other. ...
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Why does the mean for a beta distribution when input into the scipy beta cdf not return 0.5? [duplicate]

Very likely I am missing some fundamentals here, or my python coding is not up to scratch. When I use the standard formula to calculate the mean for a beta distribution ~ $B(\alpha,\beta)$ $$ \mu = \...
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Variance of beta distribution (fastest way)

Suppose a Random variable $X \sim \mathrm{Beta}(a,b)$ Find the $\mathrm{Var}( \frac{X}{1-X} ) $ My initial approach is to calculate $\mathrm{E}( \frac{X}{1-X} ) $ and $\mathrm{E}( [\frac{X}{1-X}]^...
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Bayesian inference for Beta distribution after an uncertain outcome

Normally, when we have $$p\sim Beta(a,b)$$ and an observation of $x=1$ (''success'') from a Bernoulli trial with ''success'' probability $p$, the Bayesian inference on the parameter value $p$ is $$p|x\...
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Is there a equivalence test for beta coefficients in regression analysis?

There are established ways to rule out medium/high effects like TOST for two-groups. But is there a way to rule out medium/high effects in one multiple regression? Maybe using eta-squared? What ...
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Tuning the “strength” of updates to a posterior distribution for conjugates

I'm asking this question as a sanity check- I am not a statistician or research scientist, and just am doing a gut check on a model I am building. I want to quantify uncertainty of a specific metric ...
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Multi-armed bandit where you must pull N pulls in T timesteps

Multi-armed bandit where you must pull N pulls in T timesteps Consider the beta-Bernoulli multi-armed bandit, with the following wrinkle: We have a total of $T$ time steps. We must pull $N$ pulls ...
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Fitting Beta Distributions to Data

I am trying to reproduce some beta distribution parameters found in this published paper. I have two data sets, y1 and y2, that ...
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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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LDA: weight distributions of inferred documents

I have trained a two-topic Latent Dirichlet Allocation (LDA) model on a corpus and I am now inferring on a test corpus (the nature of the corpus is irrelevant). During inference, for each new document ...
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Distribution Reference $\gamma x^{\gamma-1}$

I have been unable to find resources regarding the family of distributions with pdf $$ f_\gamma(x) = \begin{cases} \gamma x^{\gamma-1}, & \text{if } 0 \leq x \leq 1 \\ 0, & \text{...
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From beta distribution to Dirichlet: Estimation of the concentrantion parameters

Searching at least 3 hours about the connection between beta distribution and dirichlet. My problem is: I have a collection of random variables $X_i \sim Beta(a_i, b_i)$. The parameters $a_i$ and $...
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How to transform Beta distribution of second kind into Beta distribution of first kind?

! I tried to solve it in a way but I can't complete in as I don't get any idea how to integrate the Beta kind two integrand within a finite boundary.
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Uniform conjugate prior for a Beta distribution

Given $$ \pi \sim \text{Beta}(\alpha, \beta) $$ I'd like to place a prior on $\alpha$ and $\beta$. The "trick" mentioned in this post and this post seems to be to recognize that since $$ \begin{...
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Evaluating model fit for glmmTMB with beta distribution

I am looking for a way to evaluate model fit (e.g. R2, %deviance explained) for the following model: m1<-glmmTMB(AUC_indep~woody+dispersal+log_densitys+log_seedwts+I(log_seedwts^2)+(1|modeltype), ...
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Proving transformations of two independent chi-squared random variables is equivalent to a Beta distribution

I came across the following in some old class notes of mine: if $\chi_{v_{1}}^{2}$ is independent of $\chi_{v_{2}}^{2}$ then $\frac{\chi_{v_{1}}^{2}}{\chi_{v_{1}}^{2}+\chi_{v_{2}}^{2}}\backsim ...
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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
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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: ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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Squared internally studentized residual over $n-p$ is Beta distributed

Assume a regression model $y = X \beta + \varepsilon$ with $n$ observations and $p$ parameters. Let $r_i$ be the $i$-th internally studentized residual: $$r_i = \frac{e_i}{\sqrt{\hat{\sigma} (1 -h_{ii}...
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Model reputation with beta distribution

I am trying to develop a reputation score in which the reputation is calculated by the ratings that buyers give to sellers. What i am trying is to replicate a paper very well known http://faculty.neu....
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Efficiently Computing The Beta CDF [duplicate]

I am using numba to JIT compile some looped python functions as part of a larger application. Ideally, everything will run in numba's "no python" mode, such that the loop can be parallelised. One of ...
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Understanding the Bayesian question [closed]

I have a Bayesian question here: In a drug experiment, patients with a chronic condition are asked to choose between two drugs, C (control), and T (new treatment). (You may assume for the purpose ...
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What is support of beta distribution? [duplicate]

I do know that the probability density function of beta distribution is $$ \frac{x^{\alpha-1}(1-x)^{\beta-1}} {\displaystyle \mathrm {B}(\alpha,\beta)}\! $$ where $$ {\displaystyle \mathrm {B} (\...
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Can't understand the Beta distribution as described in this paper

I'm reading through the following paper (1). On page 2, section 2.1, there's a description of the selection of a beta distribution used: Since both the choice of s and the strategy for handling the ...