Questions tagged [beta-distribution]
A two-parameter family of univariate distributions defined on the interval $[0,1]$.
2
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2answers
75 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
37 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
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2answers
22 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
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0answers
27 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
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0answers
11 views
Posterior predictive for the beta distribution? [duplicate]
I'm looking to do Bayesian inference using the beta distribution.
Are there any sources for a derivation of the posterior predictive? It's an exponential family, so it should have a conjugate prior, ...
0
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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
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1answer
27 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
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0answers
21 views
Beta PDF shorth formula
Is there a closed-form solution for the shorth of a unimodal Beta probability density function? Where the shorth is the shortest interval containing at least half of the probabilities.
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0answers
15 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
54 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
136 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
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0answers
65 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
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2answers
38 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
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0answers
29 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
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1answer
26 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
52 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
76 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
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0answers
32 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
55 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
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0answers
77 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
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1answer
54 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'...
0
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0answers
34 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
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1answer
44 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
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0answers
36 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
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0answers
37 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
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1answer
99 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
126 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
146 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
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0answers
71 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
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0answers
27 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
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1answer
41 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
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2answers
415 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 ...
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0answers
121 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
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0answers
234 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 ...
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0answers
24 views
Marginal medians of the Dirichlet distribution
I am working with a 3 dimensional Dirichlet distribution with parameters $\alpha_1,\alpha_2,\alpha_3>0$. I have been trying to figure out a useful 'median' concept for this distribution. The vector ...
0
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0answers
17 views
Beta coefficient of dummy variables [duplicate]
I have a regression model with 1 quantitative variable and 2 dummy variables : y = β0 + β1*x + β2*D2 + β3*D3
How exactly do you calculate the beta coefficients of the variables in this equation ...
0
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0answers
36 views
how to get posterior distribution of beta with gamma prior
I have
$X_1, ..., X_n \sim beta(\theta,1)$ and $\theta \sim gamma(r, \lambda)$ and wish to compute the posterior distribution.
Since $f(\textbf{X} | \theta) = \theta^nx^{n(\theta-1)}$ and $\pi(\...
10
votes
2answers
326 views
UMVUE of $\frac{\theta}{1+\theta}$ while sampling from $\text{Beta}(\theta,1)$ population
Let $(X_1,X_2,\ldots,X_n)$ be a random sample from the density $$f_{\theta}(x)=\theta x^{\theta-1}\mathbf1_{0<x<1}\quad,\,\theta>0$$
I am trying to find the UMVUE of $\frac{\theta}{1+\...
3
votes
0answers
570 views
Generate Beta distribution from Uniform random variables
I need to generate random numbers from Beta distribution using random variables from Uniform distribution.
If I have two random variables $Y_1=U_1^{1/\alpha}$ and $Y_2=U_1^{1/\beta}$,
and If $Y_1+Y_2&...
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0answers
97 views
Marginal distribution of spherical uniform
For a random vector $\mathbf{X} \in \mathbb{R}^n$ uniformly distributed on the surface of a sphere of radius $r$, the PDF is the inverse of the surface
$$f_\mathbf{X}(\mathbf{x}) = 2\pi^{-n/2}\Gamma(n/...
0
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0answers
70 views
Getting shape parameters from a beta probability density
Is there a way to calculate the shape parameters $a$ and $b$ of a beta distribution having only its probability density function? This small example might clear a bit what I want (I work on Python):
<...
1
vote
1answer
57 views
Three-parameter beta function fit
I'm looking for the way to fit a three-parameter beta function on my profile data.
The data looks like this ("Data" dataframe at the end of the post):
...
0
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0answers
48 views
goodness of fit test for a beta distribution
I have a response variable that is bound by 0-1 and I would like to run a GLMM under the beta distribution. What goodness-of-fit test would be appropriate to run for data that conforms to a beta ...
2
votes
1answer
105 views
Entropy of the beta-binomial compound distribution
I have a generative process as follows:
$$
x \mid \alpha \sim \textsf{Beta}\left (\alpha,\beta \right) \\
y \mid x \sim \textsf{Bernoulli}(x).
$$
How does one go about calculating the Entropy of ...
0
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0answers
22 views
Is there a simple transform relating the generalized beta of the first kind to the GB2?
If X has a Beta distribution, then X/(1-X) has Beta distribution of the second kind (a.k.a. the Beta Prime distribution).
Does ...
4
votes
1answer
95 views
What is the likelihood function of this random variable (beta distribution parameterizing a Bernoulli distribution)?
This is related to an earlier self-study question of mine. The setup is that there are $N$ individuals, indexed by $i$, and two time periods. Individuals choose whether to "invent" something in the ...
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0answers
14 views
Transformation of Distributions
How to reduce Beta distribution of second kind into Beta distribution first kind through transformation?
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0answers
51 views
Spurious regression and autocorrelation?
I have calculated portfolio returns, using a zero cost strategy. I have data with monthly returns, that I try to explain with the Capital Asset Pricing Model (CAPM). That is, my dependent variable is ...
2
votes
0answers
99 views
Measure of relationship between two variables that are percentages containing many zeros
I am working with various different data sets (in the context of forest reclamation on industrial disturbed landscapes) that contain percent cover values of desired (planted) and undesired plant ...
0
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0answers
64 views
GLM: How to find the natural parameter when the response variable is under an arbitrary function
I'm attending General Linear Models this period. I'd like to know how do i find the natural parameter when $y$ isn't alone. Below is the exponential family form I'm working with:
$\left(\frac{y_{i}\...
