Questions tagged [beta-distribution]

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

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23 views

How to use the exponential distribution to generate samples from the chi-square and beta distributions?

I am supposed to use rexp() in R to draw from an exponential distribution with mean 1, and then use those draws to generate 1000 draws from each of the following: ...
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Beta distributed transition probability in CEA

I am reading a paper on cost-effective analysis and trying to replicate their results. (paper: https://ascopubs.org/doi/full/10.1200/GO.20.00288) The probabilistic model in the paper assumes that the ...
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Using Beta Distribution for probabilities over varying time periods

I'm running into an issue with my math not working out as expected and wondering what in my approach is causing it. I'm doing probabilistic analysis using the Beta distribution, with alpha being the &...
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Prediction of a variable that lies within the interval $[0,1]$ with masses at the ends

I have a data set on kilometers travelled by households and the associated means of transport and now want to predict a means of transport's share in households' total kilometres travelled based on ...
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38 views

How do I write out the components of my beta regression, and how do I interpret them afterwards?

I am estimating a beta-regression using the logit-link function with a continuous dependent variable bound between 0 and 1 and 5 continuous predictor variables. In R the equation is given by: betareg(...
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Creating a generalized linear model on percent/proportion data that is non-normal, heteroscedastic, and arguably zero-inflated

My objective here is to evaluate how pre-germination treatments (Pre.G) and light treatments (Light) affect percent germination (...
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29 views

What distribution would make a good hyper-prior for a Beta distribution parameterized by mean and sample size?

I have a model which includes a Beta distribution and I am looking for guidance on how to parameterize a hyper-prior for it. For example, this post uses a Beta parameterized with a mean and ...
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30 views

Replace parameter with estimate for confidence interval. Case Beta distribution

I'm trying to get a confidence interval for the mean of a beta distribution $B(\theta,1)$, using $[\hat\theta - z_{1-\alpha/2}\hat\sigma_{\hat\theta};\hat\theta + z_{1-\alpha/2}\hat\sigma_{\hat\theta}]...
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Simulating Correlated Continuous Variable Given 2 Existing Binary Variables

I am looking to draw samples from a Beta distribution (let's say α = 3 and β = 2) conditional on two existing binary variables in a correlated manner. Let's call the variable distributed as a Beta as <...
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Is there a "beta distribution" over the entire real line?

The malleability of the beta distribution pleases me; it can be symmetric, asymmetric, platykurtic and so on, as the following picture shows us: I thought it would be interesting to use it to model ...
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Distribution of the exponential of an exponentially distributed random variable?

Let $X$ be an exponentially distributed random variable, that is, with density function $f(x)=\lambda e^{-\lambda x}$ for $x\ge 0$ ($\lambda>0$), and cdf $F_X(x)=1 - e^{-\lambda x}$. What is the ...
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Expectance of predictive posterior on binomial-beta modeling

I'm struggle with figuring out how to prove: $E(\tilde{x}|x)=n\frac{a1}{a1+b1}$ where $x|\theta \sim Bin(n,\theta)$, $\theta \sim Beta(\alpha,\beta)$ and so $\theta|x\sim Beta(a_1=\sum{x_i}+\alpha,a_2=...
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Optimal number of components in a beta mixture model [duplicate]

This is a well-written blog on how we can fit a mixture of beta distributions to a dataset: http://varianceexplained.org/r/mixture-models-baseball/ However, it would have been excellent to identify ...
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69 views

Change shape parameters in a beta distribution based in each datapoint [closed]

I am new to Bayesian statistics and I have been trying to implement a Beta Binomial model from a PhD thesis in rjags. The thesis describes prior distribution for the variables but I am stuck in how to ...
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Application of spike and slab for sampling from posterior distribution (bernoulli and beta)

I think the gamma N term in the first equation relates to the spike and prior. However, I am unsure what the rhs of the first is used for? Further, I am unsure what the pie term of the second equation ...
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Inconsistent posterior estimates in Beta-Binomial likelihood vs Binomial in Bayesian, multilevel models?

In this Google Colab, I've simulated Binomial count data and compared the performance of Binomial-likelihood and Beta-Binomial-likelihood models. Both models have the same Beta prior on theta, the ...
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Beta-Binomial mixture vs Beta-Binomial multilevel model?

I first read about the Beta PDF in the context that it was conjugate to the Binomial distribution; a Beta prior with a Binomial likelihood returns a Beta posterior. So this sounds to me like a ...
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Bayesian Discrete Survival Analysis

I've been reading over Bruce Hardie's tutorial on survival analysis of customers in a discrete-time subscription model. Two design choices he delineates early on include the Geometric PMF: $P(T=t|\...
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Beta distributed dependant variable and GLM logistic link function [duplicate]

I would like to explain a continuous probability, beta distributed (U shaped) and continuous on [0,1], through a glm model with a logistic link function. Are there any concerns I should take care of ?
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Find beta from gamma distribution by inspection

I'm doing exercises in order to prepare for an exam, and have the following question: If Y has a probability density function given by f(y) = 4$y^2$$e^-$$^2$$^y$, y > 0 and 0 elsewhere. obtain E(...
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251 views

Distribution of argmax of beta-distributed random variables

Let $x_i \sim \text{Beta}(\alpha_i, \beta_i)$ for $i \in I$. Let $j = \operatorname*{argmax}_{i \in I} x_i$ (ties broken arbitrarily). What is the distribution of $j$ in terms of $\alpha$ and $\beta$? ...
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Expected Beta distribution within a group

I have a group a baseball players and I have to calculate the expected beta distribution of each player. Groups Group 1: Hits: 30, Misses: 471 -> $Beta_1(30, 471)$ = a/(a+b) = 5.99% Group 2: Hits: ...
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Copula Probability default n >= 2 case

I have been reading about Copula distributions and how they can be used to find probability of default for correlated assets. Let's say I have two assets $J$ that both have a marginal distribution of $...
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122 views

Obtain Bayes estimator with conjugate prior

Consider n observations $ X_1, X_2,....X_n $ from $ Beta_1 ~ B(1,\theta ) $ distribution. Obtain Bayes estimator for $ \theta $ under quadratic loss function when conjugate prior is assumed for $\...
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51 views

Simulating data from a beta distribution [duplicate]

I want to simulate from a beta distribution which has the following properties: The mode (peak) of the distribution is closer to 0.6. The first quartile and the third quartile should be 0.3 and 0.9 ...
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How is a convex combination of Dirichlet-distributed variables distributed?

Let $X = (X_1, \dots, X_K) \sim \operatorname{Dir}(\alpha_1, \dots, \alpha_K)$ and define the convex combination $Y = \sum_{i=1}^{K} c_i X_i$. In the case of $K=2$, the constraint $\sum_{i=1}^{K} X_i =...
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Reverse the max-min normalization of Beta/Gamma-distributed data

I normalized my data using max-min normalization as follows $$X_{normed}=\frac{X-\min(X)}{\max(X)-\min(X)}$$ How can I find the distribution of $X$ given the distribution of $X_{normed}$, if $X_{...
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How to model Beta distribution with Uniform prior in RJAGS? [closed]

I'm having trouble modeling a Bayesian problem in RJAGS. I'm analyzing depth damage curves. In 1988, the US Army Corps of Engineers estimated that 1 foot of flooding would result in 32% mean damage ...
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Interpretation of zero-inflated beta regression

I have constructed a zero-inflated beta regression model in gamlss. I find the output of this model somewhat confusing to interpret and was hoping that someone may ...
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Bayesian (continuous) logistic regression model with Beta likelihood?

I have a problem where my target variable are continuous/float values in the range [0,1]. If my data were integers in {0,1} this would be a simple logistic regression / Bernoulli likelihood problem. ...
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Given a mean, what is the range of variance values that make for possible Beta distribution parameters

The beta distribution can have its parameter estimated via method of moments, which I will be doing. $$\hat\alpha = \bigg(\dfrac{\bar x (1-\bar x)}{var(X)} - 1\bigg)\bar{x}\\ \hat\beta = \bigg(\dfrac{\...
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Transforming F-dist or long one tail

I have been going through different kaggle datasets recently to apply different techniques I have learned. I have seen loads of articles related to preprocessing your features with normalization or ...
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Finding method of moments estimate for density function $f(x|\alpha) = \frac {\Gamma(2\alpha)} {\Gamma(\alpha)^2}[x(1-x)]^{\alpha - 1}$

Suppose that $X_1, X_2, ..., X_n$ are i.i.d random variables on the interval $[0,1]$ with the density function $$ f(x|\alpha) = \frac {\Gamma(2\alpha)} {\Gamma(\alpha)^2}[x(1-x)]^{\alpha - 1} $$ where ...
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Beta distribution with a priors as Uniform and Pareto Distribution

I am working on a bayesian programming problem which involves a Beta Posterior, which has mean (location) parameter coming from Uniform Distribution [U(0,1)] and concentration (kappa) coming from ...
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Probability under Beta distribution

Let $f_a$ be the density function of a random variable $X_a$ which has a Beta distribution with parameters $na$ and $ma;$ that is, $$f_a(x) = \frac{1}{B(na,ma)}\, x^{na-1} (1-x)^{ma-1},\quad 0 \lt x \...
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Dirichlet-distribution and its correlation?

I have the following variables that follow a beta distribution: ...
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51 views

Finding a,b parameters if Highest Posterior Density is known

I know that a beta distribution with unknown parameters a,b has a 95% HPD of [0.25, 0.75]. What is the correct approach to solve for a,b?
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Setting priors for a beta distribution in R-INLA

I'm running a regression in R-INLA, where the response variable is proportion of grid squares suffering deforestation (by year, over a 20-year period). Setting the response for the last 5 years to NA ...
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What are meanings of alpha and beta in beta distribution? [duplicate]

I read some papers about beta distribution, and I saw the alpha and beta in the beta function, but what does the meaning of ...
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What are meanings of alpha and beta in beta distribution? [duplicate]

I read some papers about beta distribution, and I saw the alpha and beta in the ...
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79 views

Why is the beta distribution so flat when a, b=1?

If the beta distribution is a prior of a Bernoulli distribution (i.e. a rate of success for a binary outcome), then it is completely counterintuitive to me that the beta distribution should be ...
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1answer
56 views

Conditional beta posterior for uniform priors

I have three different random variables $\theta_1, \theta_2, \theta_3$ . These random variables are actually parameters of binomial likelihood Assume that I have prior distribution of $\theta_2 \sim ...
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1answer
252 views

How to implement a mixed-model with a beta distribution?

I am interested in using a generalised linear mixed model with a response variable (values ranging from 0.001-0.999) that best fits a beta distribution when checked using the 'fitdistrplus' package ...
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28 views

How can I choose how confident my beta distributed bayesian prior should be?

I am new to Bayesian statistics, and would appreciate help understanding the Prior. I want to combine a small national dataset with a prior from very large international studies, to give a posterior ...
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Dealing with Tall, Thin, Skewed Data

I'm working with a dataset that shows particle movement. There are three broad cases that I see in my data, when they are negatively skewed, approximately normal, or positively skewed. My end goal is ...
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1answer
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meanBEINF vs predict(model, type = "response') in BEINF GAMLSS. and determining odds of predictor variable coefficient

A variation of this question has been asked, but certain items remain unanswered - I am modeling the proportion of mortality (Prop) using a single continuous predictor variable which is temperature (...
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1answer
62 views

Beta regression or fixed effect regression

I am using panel data for 27 different countries in 5 different time periods. My IV and DV both are in fractional form (0,1), i.e., in percentages. Please guide me, if beta regression is appropriate ...
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237 views

Bayesian point estimate of a random sample

I am new to statistics and some concepts are not clear to me. I have a random sample that is distributed as a Binomial with parameters $k=2$ and $\theta$ unknow. Using a Bayesian approach I must give ...
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Dependent Variable only fall between 0 and 1 (bimodal with peak 0 and 1). I need to use OLS with Beta transformation model

Dependent Variables only fall between 0 and 1 (bimodal with peak 0 and 1). I need to use OLS with the Beta transformation model. I need to perform OLS regression, for that, I have to do the ...
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58 views

how to get beta prior distribution based on given CI?

If given a 95% CI with lower and upper bound, and the mean. The mean is not centered in the CI. How to calculate apha beta in Beta Distribution?

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