# Questions tagged [beta-distribution]

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

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### Distribution of product and sum of beta random variables

I have a set of probabilities that I am modelling as (independent) $p_{A,i} \sim Beta(\alpha_{A,i},\beta_{A,i})$ and $p_{B,i} \sim Beta(\alpha_{B,i},\beta_{B,i})$. I am calculating the following ...
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### Distribution of the correlation coefficient based on quadratic forms

Let $x,y$ be two independent random correlated vectors following the same multivariate (real or complex) centred normal distribution, and let $A$ be a non-negative linear operator. We can read here, ...
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### How to approach GLMs using data with beta distribution in R?

I'm trying to run some models on bee presence with five predictor variables. A snippet of the data is attached, but essentially I measured floral abundance and richness, calculated floral evenness and ...
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### Need help in calculating $\mathbb{E}(\frac{1}{x_{(2)}-x_{(1)}}\int_{x_{(1)}}^{x_{(2)}} f(t) \ dt)$, where $x_{(i)}$ are related Beta distribution

Suppose $Y, Z \stackrel{\text{iid}}{\sim}\mathrm{Uniform}(0,1)$. Let $a = g(\min(y,z)),\ b=g(\max(y,z)).$ How can I calculate the expectation $$\mathbb{E}\left[\frac{1}{b-a}\int_a^b f(t) \ dt\right]$$ ...
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### F test to compare variances. How is ncp calculated to obtain the F distribution under the alt hypothesis?

Recently I needed to do a power analysis for a comparison of variance with a F test. In the past I used the OC curves from Edwin Crow's "Statistics Manual" Chart VIII to get beta. https://...
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### How to resolve the residual versus predicted quantile devation (Dharma plot)?

I have been trying to perform beta regression modeling with random effects. I have sex ratio (0.561, 0.765 etc) as the response variable, and climatic variables + years (1970-2021) as predictor ...
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### How to check if a set of numbers matches a Beta (4,4) distribution?

I have a random number generator that should generate values based on a Beta 4,4 distribution and some minimum and maximum. (IE, values between 0.9 and 1.1) I can generate a large set of numbers using ...
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### Why do many people like to use "normal distribution" instead of $\beta$ distribution when the theoretical range of data is finite?

Say we are approximating the distribution of the test score of a large group of students, while the theoretical minimum score is 0 and the maximum is 100. In this case, many people use the normal ...
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### Can Phi coefficient for intercept be negative?

I am working on beta regression model with two grouping variables (farm and years). Climatic variables are my predictors. Response variable is male proportion. I standardized all variables prior to ...
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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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1 vote
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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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### 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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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 ...