Questions tagged [beta-distribution]
A two-parameter family of univariate distributions defined on the interval $[0,1]$.
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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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1answer
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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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1answer
54 views
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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2answers
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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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1answer
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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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2answers
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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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1answer
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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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1answer
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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:
...
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1answer
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How to model a binary vector by the Beta-Bernoulli distribution in R or Python？
I have a set of data $x=(x_1,x_2,x_3,...)$;e.g:$x=(0.1,0.003,0.78,...)$
which follows a beta distribution. Since $x_i$ in my data $x :x_i ~ Bernoulli(p)$, where $p$ is the prior of average $x$ and ...
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Simulate a 2D-beta distribution: spatial simulations
I'm doing spatial simulations and I would like to simulate a matrix that represent a truncated 2D-bimodal distribution with U shape. In other words, I would expect high density towards the borders of ...
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1answer
173 views
How to pick starting parameters for MASS:fitdist() with the beta distribution?
I have data set of ~700k yes/no events that I want to first aggregate on various features (e.g. group by average), always resulting in a 34 length vector. From there, I want to fit a beta ...
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1answer
141 views
Finding the distribution of sample range for a Beta population
Let $X_1,X_2,\ldots,X_n$ be i.i.d random variables having density
$$f(x)=2(1-x)\mathbf1_{0<x<1}$$
I am trying to derive the distribution of the sample range $R=X_{(n)}-X_{(1)}$.
The ...
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How to infer a prior belief after observing a behavior
My participant goes through a maze made of 32 T intersections. At each intersection he must choose whether to go either to the left or to the right: one option will lead to another T intersection, ...
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2answers
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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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calculating credible intervals for Bernoulli trials with a beta-distribution
I'm interested in finding credible intervals for Bernoulli trials with a variable probability of success.
So, the process (as I understand it) is the probability of success, p, is modeled with a ...
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1answer
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how can this missing observation model be extended to include cases where sigma is a function of other variables?
Richard McElreath's blog entry Algebra and the Missing Oxen describes a simple missing observation model in RStan. At the end of the blog, he says it can be extended easily to cases in which the ...
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1answer
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Issues with qbeta and pbeta [closed]
I'm trying to get samples from truncated beta. I have written the following function
based on inverse transform sampling method to do so, however, it seems that when CDF converges to 1 fast, pbeta ...
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1answer
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Beta Distribution and how it is related to this question
Let $f(x) = k(\sin x)^5(1-\sin x)^7$ if $0 \lt x \lt \pi/2$ and $0$ otherwise. Find the value of $k$ that makes $f(x)$ a density function.
I'm struggling to understand how this relates to the Beta ...
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Parameter Estimation with Method of Moments
I was working on some problems and came across this one I was having trouble with:
Given a random sample {0.1, 0.4, 0.2, 0.1} from a Beta population with β = 1, use the method of moments to find an ...
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2answers
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PDF of incomplete beta function
I have a (probably) biased coin. I want to make a Bayesian inference on $\lambda=p(coin=\text{heads})$. I define my prior $p(\lambda)\sim Beta(\lambda; a=1,b=1)$. I toss the coin and update my ...
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How to obtain cumulative distribution function for a specific probability density function via R
I have the following probability density function.
$$f(x,y) = \dfrac{1}{B(a,b,c)}\dfrac{x^{(a-1)}y^{(b-1)}(1-x)^{(b+c-1)}(1-y)^{(a+c-1)}}{(1-xy)^{(a+b+c)}}$$
I wrote the following ...
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1answer
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Simulate Bivariate Beta Distribution , BIBETA(6, 20, 2) in R
I need to simulate bivariate beta distribution, $BIBETA(6, 20, 2)$ in r. I am looking for a package/ code that would generate bivariate beta distribution. I couldn'...
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How to specify a zero-inflated Dirichlet model in JAGS/BUGS
There was a recent publication discussing the advantages of the zero-inflated dirichlet for microbiome count data which is compositional (you are modeling a matrix of species relative abundance data ...
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1answer
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Joint Posterior Distribution
I have 4 groups, each has a probability of developing gout (Bernoulli distribution), with a total of 400 individuals. I am confused how to derive and present the joint posterior distribution for each ...
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Conditional and marginal R2 with mgcv
I am fitting a beta regression model with random effects using the mgcv pacakge in R. This package only provides an adjusted R-square. Is there any way to also get conditional and marginal R2 values ...
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fraction below range for normally distributed population
We have months of continuous glucose sensor data from hundreds of subjects, sampled every 5 minutes. For each subject we calculate $\mu$ and $\sigma$ (normal distribution). For the entire subject ...
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1answer
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Trouble specifying a hierarchical dirichlet model in JAGS
I have a sampling design where samples (cores) are taken within plots. Those plots are then nested within sites. There are multiple sites. I would like to get a hierarchical site-level estimate of ...
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1answer
153 views
Convert normal random variable into beta random variable in STATA
I need to generate two random variables - lognormal and beta distributed - while ensuring that the correlation between the two variables is -0.3.
I generated two normal random variables with -0.3 ...
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Bayesian Statistics. Please help me to find an example where posterior variance is greater than prior variance
Suppose we observe y successes in n trials where the probability of success in each trial is θ. If we choose a Beta(1, 1) (Uniform) prior then the posterior variance will be smaller than the prior ...
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Simulating by hand the predictions of a complex mixed model with beta distribution from glmmTMB for diagnostic
I am conducting a GLMM for a meta-analysis using the beta distribution with the package glmmTMB. My response variable is a vector of correlations (No exact 0 or 1), but Fisher’s transformation fails ...
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What is the difference between each predictor's standardized betas (from multiple regression) and it's Pearson's correlation coefficient?
Say we have a multiple regression model with three predictors and one outcome variable.
Each predictor has it's associated standardized beta, which tells you how many standard deviations the outcome ...
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1answer
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Updating the parameters of a Beta distribution in a “real life” situation
I know this is a contrived example but I am trying to understand how to use Bayesian statistics and I need your help with my doubts.
Let's say I am visiting an island where I know there are a million ...
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2answers
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What's the intuition for a Beta Distribution with alpha and / or beta less than 1?
I am curious for myself, but also trying to explain this to others.
The beta distribution is often used as a Bayesian conjugate prior for a binomial likelihood. It is often explained with the example ...
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glmmTMB in R beta regression or Poisson distribution?
I have a data set which is very zero inflated. Zeros are representative of true zeros, meaning that in this case a zero is a legitimate value to have indicating something about the individuals tested (...
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R-squared for glmmTMB with beta distribution and logit link
I'm looking for a method or function for computing R² for glmmTMB models with a beta distribution and a logit link. I am interested in a ratio (%) response in a repeated measures design.
I looked ...
