Questions tagged [beta-distribution]
A two-parameter family of univariate distributions defined on the interval $[0,1]$.
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What is the posterior probability for flipping a coin, assuming a beta distribution as conjugate prior
Suppose, I toss a fair coin n = 10 times and get 7 heads and 3 tails. The probability of fair coin is p = 0.5. Now, that the beta distribution is a conjugate prior of the binomial likelihood. I used ...
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Can a softmax probability distribution be approximated to Beta distribution?
I am wondering if attention weights in BERT language model layers ( which ,in essence, are softmax probability distribution) can be approximated with beta distribution? With approximated beta ...
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Does this type of distribution have a name?
I have some integer data, produced by slightly convoluted numerical procedure, which is distributed between $0$ and $300$, with the most probable values being $0$ and $300$, and the least probable ...
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Interpreting y axis in density plot
200 people were tested, 20 of those were infected. I want to get a posterior distribution for the uncertainty associated with the probability that a person is infected.
I do this like this:
...
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Comparability of means for non-normal distribution and small sample size
I have to perform a comparability study between pre and post change of a production process.
I'm using the final purity to measure comparability and wanted to compare medians between pre (n=40 runs) ...
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Approximating the distribution of the product of iid beta variates
Background
I am interested in the distribution of
$$\theta_0=1-\prod_{i=1}^n(1-\theta_i)$$
where the $\theta_{i>0}$ are iid beta random variates:
$$\theta_{i>0}\sim\text{Beta}(\alpha,\beta)$$
In ...
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How to interpret odds ratios by emmeans for glmmTMB-beta
I fit this mixed model with beta for the response variable: photochemical efficiency or Fv/Fm and the predictor variables are categorical:
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Model predictions are under-predicting on the high end of the distribution [duplicate]
I am trying to create a linear model where the dependent variable has the following summary features:
Min
1st Qu.
Median
Mean
3rd Qu.
Max
0.1579
0.3155
0.3547
0.3459
0.3827
0.4583
There were some ...
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Updating a Beta prior based on observations from a product of two Independent Bernoulli variables
I'm working on a problem involving Bayesian updating with a Beta prior, but the data I observe comes from a slightly complex source.
Let $X \sim \text{Bernoulli}(p)$ and $Y \sim \text{Bernoulli}(q)$, ...
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Fitting data with a beta distribution using fitdist from fitdistrplus package in R
I have a variable x that corresponds to data from a database. I've been trying to find the best distribution to fit it and looking at the histogram I figured either a normal, weibull or logistic ...
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Why does MCMC estimate the variance in a logit-normal model incorrectly?
I am trying to estimate the variance $\varepsilon^2_X$ in a simple logit-normal model of the form
$ \sigma^{-1}(U) \sim \mathcal{N}(\mu_U, \varepsilon^2_U)$
$ \sigma^{-1}(X) \sim \mathcal{N}(\sigma^{-...
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Bounded Distribution with specific limits regarding Variance
Im currently looking for a probabilty density function that posesses the following properties
Should have range (0,1)
$$
\lim_{\sigma \rightarrow 0} f(x) = \delta(1)
$$
$$
\lim_{\sigma \rightarrow \...
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Resulting beta distribution from two different samples
Let’s say each sample consists of 300 units inspected for defects.
I have historic data from 100 samples in the past that give me an idea of what I expect the defect rate to be.
I have a new batch to ...
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Mixed beta regression interpretation with categorical predictor
I have run mixed beta regressions on proportional data but I am struggling in my interpretation of the results. I understand this has been asked before but I have a categorical predictor with four ...
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Zero- and one-inflated beta GAMM (Generalized additive mixed model) in mgcv
I have vegetation cover (%) data [0,1] that includes 0's and 1's that I'd like to model with a beta GAMM, but don't understand the method for doing so. I've read that if the data includes 0's and 1's ...
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How to interpret the DHARMa quantile residual plot?
We calculated a GLMM based on the beta distribution:
...
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Thompson Sampling with Two objectives - Cost and Success Rate
I have implemented a Thompson sampling algorithm with beta distribution that chooses between two processors to process the payments for each transaction such that it maximizes the success rate. For ...
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Let X is beta distributed, what is the distribution of 1/X?
Let $X \sim Beta(a,b)$. I was wondering what is the distribution of $\frac{1}{X}$?. Here is my derivation by using transformation of random variable.
Let $Y = h (X) = \frac{1}{X}$, which implies $h^{-...
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Bounded variable: beta regression or switch to ratio?
My task is to study factors that influence the composition of labor force. The latter consists of two types of workers, full-time and part-time. My first approach was to run an OLS regression for the ...
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Calculating the parameters of a Beta distribution using the harmonic mean and variance
Is there a similar way to this for calculating the $\alpha$ and $\beta$ parameters for a Beta distribution if I know the harmonic mean and variance that I want the distribution to have ($\alpha>1$ ...
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Power of Uniform Order Statistics
I know that if $U$ is a uniform r.v. in $(0,1)$, then $U^a\sim Beta(1/a,1)$ with $a>0$.
On the other hand, if $U_{(1)}\leq \cdots\leq U_{(n)}$ are the uniform order statistics, then, with $U_{(0)}=...
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Distribution of product of Beta and Chi-Squared?
If $X$ is distributed as Beta distribution and $Y$ as Chi-Squared, does the distribution of $Z = X Y$ have a name?
For instance if $X\sim \text{Beta}\left(\frac{1}{2},1\right)$ and $Y\sim \chi^2(1)$, ...
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How to report emmeans results when p value = 1.00?
I am working with data of vegetation cover (proportions) for different height strata (0-5, 5-15, 15-30, >30 cm, and also bare ground) amongst four different sites and two different time periods (...
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When can we assume a particular distribution in a statistical model?
In statistics, we often assume that a particular variable follows a certain distribution. For example, if we know $Y \in \{0, 1\}$, then we can assume $Y \sim \text{Bernoulli}(p)$, since using the ...
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Why does dbeta not sum to 1?
Both dpois and dnorm in the code below sum to 1 (or thereabouts). This appears to confirm my understanding of the ...
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MLE fit for beta distribution given vector of rates?
Say that I have a vector of success rates, which are each ratios bound by [0,1]. I know how to get a normal approximation of this data; however, I'm interested in getting the MLE fit for Beta(a,b) ...
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Performing a power analysis on finding the mean of a single sample, non-normal dataset
I would like to perform a power analysis on my pilot data. My test statistic is a single-sample mean with only 14 observations. The data are non-normal (it's percent vegetation cover, which I think ...
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Capturing increased uncertainty as data changes
I'm experimenting with quantifying uncertainty in data from a Bernoulli distribution by measuring the likelihood the p parameter using the beta distribution. Specifically, I'd like to show how ...
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RJAGS - Bayesian Beta binomial syntax
I am working on a classic problem when the posterior probability distribution of a proportion must be obtained. This parameters is assumed to followed a beta distribution, therefore the number of ...
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Beta prior for the Clopper-Pearson interval
A binomial sample of $n$ trials consists of $k$ successes. The distribution of $k$ is
$P(k|\theta, n) = C_n^k \theta^k(1-\theta)^{n-k}$
We would like to construct a confidence interval for the ...
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Testing relationship between exponential and beta distributions using R
If X ~ Exp(3), Y ~ Exp(1) and h = X / (X + Y) then h ~ beta(1/3, 1) and E(h) = 1/4.
But when I draw random deviates using the following R code, I find mean(h) ≈ 0.324 and the histogram doesn't ...
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Does a single observation from a population have the same distribution as that population?
Suppose X1 is one observation from a population with Beta(θ,1) PDF. Would X1 also have Beta(θ,1) PDF?
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How could I evaluate $A = \int_0^1 \log\left(\theta^s(1-\theta)^{n-s}\right)p(\theta)d\theta$?
Suppose that I want to evaluate the following integral:
$$A = \int_0^1 \log\left(\theta^s(1-\theta)^{n-s}\right)p(\theta)d\theta,$$
where $p(\theta)\equiv$ Beta$(ws+1, w(n-s)+1)$ and $n$, $w$, and $s$ ...
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For a binary outcome, is the distribution necessarily Bernoulli? Could, for instance, "beta-Bernoulli be in play?
When a variable is binary, it sure seems like its distribution is totally characterized by the probability of being in one group: the variable takes one value with probability $p$ and the other value ...
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How to choose the input parameters for a Beta-Pert distribution if no expert estimates can be elicited?
The Beta-Pert-Distribution is often used to model uncertainty in risk management. It takes three values a minimum, maximum and most likely (mode).
Generally, these numbers ought to be provided by ...
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Interpretation of Beta Family in Generalized Additive Model (GAM)
My code for generalized additive model with the beta family.
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Interpreting coefficients of beta regression
I have implemented a beta regression and am a little confused on how I should interpret the coefficients of my model. For context, both my independent variables and dependent variable are expressed in ...
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Use of the Beta-Binomial Distribution in Capture-Recapture Sampling
During capture-recapture sampling, we aim to estimate a population size (e.g. of organisms) by capturing a sample of size $ n_1 $, marking them, releasing them, then re-sampling (assuming they have ...
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How can I compute the joint distribution function of normal distribution and beta distribution? [closed]
In my problem, I have a condition in which I need to compute the joint distribution of two dependent distributions. The first distribution is normal and the second one is beta distribution. How can I ...
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Factor Analysis: Simulating observations from predetermined factor loadings with beta-distributed variables
I have a question about simulating data in the context of (exploratory) factor analysis.
I need to simulate n observations of p measurable variables derived from k latent variables given factor ...
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Expected value of the log of the sum of beta distribution
Can someone help me compute this expression:
$$E[\log(X Y + (1-X)(1-Y))]$$
where $X\sim\operatorname{Beta}(a_1,b_1)$ and $Y\sim\operatorname{Beta}(a_2,b_2)$, and where $X$ and $Y$ are independent.
In ...
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Does beta logit model assume dispersion like Poisson or in Binomial model?
I would like to know what are the assumptions of a beta logit model and more particularly does it assume certain dispersion. In other words, does one speak about over and under dispersion for beta ...
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Does the uniform distribution $U(1,n)$ have an equivalent Bernouli or beta distribution form?
For a uniform distribution on the interval between $0$ and $1$, there is a $Beta(1,1)$ and Bernouli distribution $ Bernouli(1, 0.5)$ that can describe this. What parameter values for the Beta and ...
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Sampling From Four-Parameter Beta Distribution
Most statistical computing packages have functions to sample out of a two-parameter Beta distribution, but not many offer functions for sampling out of a four-parameter Beta distribution. If I want to ...
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Can you create Kalman filter (or a recurssive state estimator) with Beta and Binomial distributions?
I have to infer the probability of a system failing from observations. Since probabilities are bounded between 0 and 1, they are sometimes modeled using Beta distribution. While the traditional Kalman ...
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On the difference between two independent beta distribution
This is a follow up to this question. Consider again two independent rvs $X\sim Beta(a_1+1,b_1+1)$ and $Y \sim Beta(a_2+1,b_2+1)$. Here $a_1,b_1,a_2,b_2$ are in $\mathbb{N}$.
Is it true that $\mathbb{...
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Property of two independent Beta distribution
I have been working with beta-bernoulli posteriors recently. Is it true that if $X,Y$ are independent rvs with $X \sim Beta(a_1+1,b_1+1)$ and $Y \sim Beta(a_2+1,b_2+1)$ then $\mathbb{P}(X>Y)>0.5$...
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Adjustments in Bayesian inference
I have $P$ as a random variable with the prior $P \sim N(p, \sigma)$, where these parameters are known. Let $p_1$ and $p_2$ be two unknown values from $P$. I am trying to estimate both of them using ...
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PyMC3 Beta-Binomial fails to converge on actual parameter values
Something is not performing as expected with PyMC. I'm trying a simple Beta-Binomial conjugate prior model, trying to recover known parameters.
Control data
...
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What is the intuition behind quantile in scipy.stats.beta.ppf? [closed]
I'm trying to use scipy.stats.beta.ppf(q, a, b), where q is referred to as quantile. I understand how beta works and its details, but I'm not able to make sense of ...
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