# Questions tagged [beta-distribution]

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

666 questions
Filter by
Sorted by
Tagged with
1 vote
66 views

### 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 ...
14 views

### 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 ...
226 views

### 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 ...
31 views

### 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: ...
19 views

### 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) ...
69 views

### 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 ...
45 views

### 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: ...
1 vote
40 views

### 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 ...
125 views

### 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 $Y \sim \text{Bernoulli}(q)$, ...
31 views

### 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 ...
29 views

169 views

### 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 $\mathbb{P}(X>Y)>0.5$...
25 views

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 ...