Questions tagged [beta-distribution]

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

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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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Bayesian A/B testing with parameters other than success rate

If I have certain number of clicks and conversions for a group of ads, I can do Bayesian A/B testing following this method http://ucanalytics.com/blogs/bayesian-statistics-to-improve-ab-testing-...
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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 of Beta ( Taylor series)

Suppose X is a random variable with a Beta ( a =$\frac{1}{2}$ , b=1) distribution and x in (0,1) Then the moment generating function is calculated as below $ M_X(t) $ = $\mathbb{E}[e^{tX}]$ =$ \...
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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 ...
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Distribution of dot products of two random independent unit vectors in $D$ dimensions

Duplicate of the stats stack exchange question here; however, I need some help with some of the steps in the accepted answer. A uniform distribution on the unit sphere $\mathbb{S}^{D-1}$ is ...
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Proportion/Rate data and zero-inflation (two counts)

I have an experimental dataset which makes use of two counts. Using vague terms, we are studying animals as they become behaviourally inactive and then apply a stimulus once an hour. One of the counts ...
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How to relate beta CDF to student-t CDF? [duplicate]

We can relate the student-t and beta distributions as such: If $X$ has a Student's t-distribution with degree of freedom $\nu$ then one can obtain a Beta distribution: $$\frac{\nu}{\nu + X^2} \...
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Interpretation very small standardized coefficient beta

In one of my studies I have results similar to the below: β=-0.0007 (95% CI: -0.0009, -0.0002), p=0.01 Since β is so small (but also the Confidence Interval (CI)), is this result still meaningful? ...
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In a manuscript, is an incomplete beta function a useful simplification of a sum, if the argument ends up negative?

I'm working on a manuscript which I intend to submit to a statistics journal. I have a sum which I "simplify" to the regularized incomplete beta function $I_{-t}(a,b)$, where $t$ is a positive real ...
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Can I improve an estimate of a coin-flip probability from a single trial using an imperfect oracle?

I have the following generative model: I have a unknown random variable $S\in[0,1]$ and samples $s_i \sim S$. I do not observe $s_i$ directly, but instead an imperfect oracle $q_i$, which might or ...
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Appropriate statistical test for continuos bounded r.v

I have a number of continuous random variables bounded in the domain [0,b] and I need to perform a statistical test to check whether their average is different from ...
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Beta-binomial distribution for scaled and translated Beta

Recall, that a binomial distribution in which the probability of success at each trial is randomly drawn from a beta distribution results in the so called beta-binomial distribution. One can calculate ...
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Why p-values are not significant even though AIC values improved a lot in model selection using GAM mix modelling and beta regression

Dear StatExchange community, I am studying disease progression in plant leaves and I am trying to estimate differences between a wild-type and a mutant plant. To achieve this I am using the ...
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In a bivariate normal sample, why is the squared sample correlation Beta distributed?

If $(X_i,Y_i), i = 1, \dots, n$ are independently bivariate normal distributed, with mean $(\mu_x , \mu_y)$ and variances $(\sigma_x^2, \sigma^2_y)$ and correlation coefficient $\rho = 0$. Denote $T =...
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Simulate from a mixture of two beta distribution [closed]

I have this distribution : $X \sim 0.75\mathcal{B}e(\alpha_{X_1}=1,\beta_{X_1}=3)+0.25\mathcal{B}e(\alpha_{X_2}=5,\beta_{X_2}=1.75)$ where the density function is given from this function: ...
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Mean of a truncated non-standard beta distribution

I have a non-standard beta distribution in the interval [-0.02 , 0.005] (as opposed to [0,1]). I know its mean and variance (and thus α and β). I want to calculate the mean of its truncation to [0 , ...
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All positive Beta exponents in a binomial logistic regression

I'm running a regression in which the predictor is a categorical measure of living arrangement (1=two parent household, 2 = single parent, etc). There are 8 total categories in this variable. I'm ...
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Question regarding FamaMcBeth regression

I'm new here and hope you can help me with three questions I'm having in regard to the FamaMcBeth regression methodology. What is the advantage of using firm specific returns instead of an aggregate ...
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Change point detection in beta distribution

If the outcomes of agent is modeled as a Bernoulli distribution with success probability θ ∈ [0, 1]. Where α is number of successful tasks that agent execute, and β is number of unsuccessful tasks ...
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Power Analysis with Noncentral F distribution

I'm looking to replicate a power analysis for binary data using an MRMC analysis (details found here). The data looks like this, where Score is a binary variable. ...
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Probability that one random variable using the Beta Distribution being greater than another, bounded intervals

I am doing some practice problems to prepare for my statistics exam, and I just want to know if my reasoning is correct on one problem, and if not, I want to know how I should reason through this. The ...
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Independence of Beta ratios of Gamma variates

If $X= x_1/(x_1+x_2+x_3)$ and $Y= x_2/(x_1+x_2+x_3)$ where $x_1, x_2, x_3$ are independent $\chi^2$-distributed random variables with d.f. $-n_1,n_2, n_3$ respectively. Are $X$ and $Y$ independent? I ...
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How to justify using Beta distribution as a prior distribution in the following problem

Let $\theta$ be the proportion of people who are ready to quit smoking within 6 months. Let's say we perform a survey in $2017$ with a $n$ volunteers who ask people this question until they obtain yes ...
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Beta distribution and normalization [duplicate]

Here in the 4 pictures in the last answer, is the vertical axe the probability? I.e. it seems to me that it is somewhat unnormalized : it has the value 2 in the 2nd picture and 3 in the 3rd picture. ...
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Self Study - How does $\alpha$ and $\beta$ correspond to mean and variance of a beta distribution? [duplicate]

I am trying to figure out how to provide $\alpha$ and $\beta$ in terms of $\mu$ and $\sigma$ in a beta distribution. $\mu$ is given as $\mu = \frac{\alpha}{\alpha + \beta} $ $\sigma$ is given as $\...
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Analysis in a beta simulation

I did a simulation where shape1=1 and shape2=2, for n=10, n=100 and n=1000, the following is: ...