Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [beta-distribution]

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

1
vote
0answers
45 views

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 ...
1
vote
0answers
45 views

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 ...
0
votes
1answer
17 views

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 ...
1
vote
0answers
14 views

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} \...
2
votes
2answers
32 views

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? ...
0
votes
0answers
18 views

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 ...
0
votes
0answers
8 views

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 ...
0
votes
0answers
13 views

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 ...
4
votes
0answers
27 views

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 ...
3
votes
1answer
43 views

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 ...
1
vote
0answers
37 views

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 =...
0
votes
1answer
46 views

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: ...
1
vote
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 , ...
0
votes
2answers
26 views

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 ...
1
vote
0answers
28 views

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 ...
0
votes
0answers
28 views

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 ...
0
votes
0answers
18 views

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. ...
1
vote
1answer
31 views

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 ...
0
votes
2answers
84 views

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 ...
0
votes
1answer
44 views

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 ...
0
votes
2answers
28 views

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. ...
0
votes
0answers
36 views

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 $\...
0
votes
1answer
11 views

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: ...
1
vote
1answer
36 views

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 ...
0
votes
0answers
19 views

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 ...
1
vote
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 ...
7
votes
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 ...
4
votes
0answers
68 views

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, ...
0
votes
2answers
45 views

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 $\...
0
votes
0answers
40 views

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 ...
0
votes
1answer
31 views

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 ...
2
votes
1answer
60 views

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 ...
6
votes
1answer
79 views

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 ...
0
votes
0answers
33 views

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 ...
0
votes
2answers
59 views

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 ...
0
votes
0answers
84 views

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 ...
-1
votes
1answer
85 views

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'...
1
vote
0answers
53 views

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 ...
0
votes
1answer
72 views

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 ...
0
votes
0answers
51 views

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 ...
0
votes
0answers
40 views

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 ...
0
votes
1answer
125 views

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 ...
2
votes
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 ...
1
vote
1answer
204 views

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 ...
0
votes
0answers
77 views

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 ...
1
vote
0answers
28 views

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 ...
4
votes
1answer
59 views

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 ...
2
votes
2answers
704 views

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 ...
0
votes
0answers
157 views

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 (...
0
votes
0answers
333 views

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 ...