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

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17 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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11 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 ...
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1answer
13 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
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1answer
128 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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0answers
63 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, ...
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2answers
34 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 $\...
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21 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 ...
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1answer
24 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 ...
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36 views

Robust (Newey West) beta, covariance and variance

Let's start with a simple linear model $$Y_t = β_0 + β_1*X_t + ϵ_t$$ If $ϵ_t$ is serially correlated and heteroskedastic, I can calculate N-W standard error of $β_1$. I have also read in the ...
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1answer
45 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
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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 ...
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26 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 ...
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2answers
54 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 ...
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0answers
60 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 ...
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1answer
43 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'...
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0answers
25 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 ...
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1answer
28 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 ...
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0answers
31 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 ...
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0answers
35 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 ...
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0answers
22 views

Determine sample size of beta distribution to detect a difference in means to a second beta distribution for a particular confidence level.

I try to understand how a former colleague of mine came up with the answer to the following question. We have two Beta distributions with the first one having $µ_1$ = 0.2, $\sigma_1 \approx 0.02$ ...
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2answers
74 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 ...
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1answer
96 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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1answer
127 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 ...
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49 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 ...
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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 ...
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1answer
37 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 ...
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2answers
273 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
75 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 (...
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0answers
154 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
20 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 ...
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0answers
16 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 ...
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29 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(\...
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2answers
307 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+\...
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0answers
413 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
77 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/...
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42 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): <...
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1answer
48 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): ...
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40 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
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1answer
90 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 ...
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0answers
21 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 ...
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1answer
88 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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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
44 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
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0answers
74 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 ...
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0answers
58 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}\...
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0answers
49 views

Tight bound for Binomial distribution or, equivalently, the Incomplete Beta function?

Suppose $X \sim Binomial(n,p)$ with known $n$ but unknown $p$, and let $G(p,k) = P[X \geq k)$ for $k=0, \ldots, n$. I am looking for a tight upper bound on $|G(p_1, k) - G(p_2, k)|$ for some given $k$....
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20 views

Question about normal probability plot using different data

I tried to plot different types of randomly generated data in a normal probability plot. Why is it that all data seem on the line on at least some part? The Beta(0.5,0.5) seem to follow the line very ...
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1answer
36 views

Mean values of the prior and posterior distributions [closed]

I'm having trouble understanding the mean values for a prior and posterior distributions. I know a beta distribution can be found by: α / α+β . Can a prior or posterior value be found using the same ...
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1answer
199 views

Specifying a beta prior distribution

I need help trying to understand how values can be used in a beta distribution to represent priors/posterior probabilities. I'm aware that there are similar questions that have already been asked ...
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27 views

Combine pdfs from generalized beta prime distributions

A model I'm working with produces a numerical posterior distribution that follows a generalized beta prime distribution. I'm attempting to combine several of these distributions to quantify ...