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

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1answer
22 views

Univariate priors for the parameters of a Beta distribution

I need a rather a prior on the parameters of a Beta distribution (i.e. $\alpha$ and $\beta$). I have an external constraint that requires me to use univariate priors, one for $\alpha$ and one ...
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0answers
4 views

Interpreting results of mediator analysis

I need help to understand the results of my mediator analysis. The DV was dichotomous, IV and mediator have interval scale. The calculated b's were all significant but when I calculated the β, I got ...
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1answer
58 views

Remove effect of a factor on continuous proportion data using regression in R

I have a data set of continuous proportions which depend on a fixed-effect factor, e.g.: ...
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0answers
16 views

Mode of the difference of two beta distributions

Given two beta distributions $X \sim \beta(m_1, n_1)$ and $Y \sim \beta(m_2, n_2)$, how to compute the mode of the distribution of $Z = X - Y$?
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1answer
213 views

Expected value of a random variable

Random variable $X$ has the probability density function \begin{equation*} f\left( x\right) =\left\{ \begin{array}{ccc} n\left( \frac{x}{\theta }\right) ^{n-1} & , & 0<x\leqslant \theta ...
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0answers
19 views

Approximation for linear combination of truncated beta variables

Let $x_1, x_2$ be random variables that follow truncated beta distributions: ...
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0answers
7 views

How to measure whether the YES/NO (Bernoulli trials) answers have converged about their estimated mean for a specified error bound?

I have a questionnaire with questions that require a Yes or a No answer (1 or 0 input) from participants. From the set of answers I want to use the mean, $\mu$, estimated from the data for the ...
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0answers
33 views

estimating product of 2 independent variables

I have 2 independent variables with distributions: $X \sim \text{beta}(\alpha_1,\beta_1)$ and $Y \sim \text{beta}(\alpha_2,\beta_2)$ I would like to estimate $P(X * Y >= \text{val})$, and I am ...
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1answer
29 views

What is the distribution of a sum of a subset of probabilities, with each probability having the same distribution?

Suppose I have k outcomes with probabilities, pi, with p1+p2+...+pk=1. Each probability has the same distribution. What would the distribution of a sum of probabilities be? For example, what would the ...
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0answers
22 views

Hypothesis testing for cost-per-click metrics

I have two ads, and I want to figure out which is better. If they both have identical cost, my null hypothesis is that the probability of success in the first is equal to the second, and I can use ...
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3answers
59 views

What probability distribution is to the discrete uniform distribution as the beta distribution is to uniform distribution over $[0,1]$?

A beta distribution with its parameters $\alpha = \beta = 1$ is the uniform $[0, 1]$ distribution. What distribution is to the discrete uniform distribution (the sample space is left undecided), as ...
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0answers
102 views

Distribution of the ratio of dependent chi-square random variables

Assume that $ X = X_1 + X_2,...+ X_n $, where $\; X_i \sim N(0,\sigma^2)$ and independent. My question is, what distribution $$ Z = \frac{X^2}{X_1^2 + X_2^2 + ... + X_n^2} \;\;\; (1)$$ follows. I ...
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40 views

Scaling the backward variable in HMM Baum-Welch

I am just trying to implement the scaled Baum-Welch algorithm and I have run into a problem where my backward variables, after scaling, are over the value of 1. Is this normal? After all, ...
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2answers
61 views

Beta distribution on discrete data

Suppose that my data $y \in \{0,0.1,\ldots,1\}$. What are the consequences of modeling that data as continuous, i.e., as if $y \in [0,1]$, by using the beta distribution? Is there a version of the ...
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0answers
41 views

Multivariate Beta distribution (no Dirichlet!)

What is a multidimensional generalization of the Beta distribution, in compliance with the following specification? I am not looking for the Dirichlet distribution. I am looking for a generalization ...
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0answers
41 views

Hierarchical model: question on frequentist estimation

I am interested in understanding the differences between Bayesian and Frequentist estimation in the context of hierarchical models. Consider $n$ subjects, where for subject $i$ there are $k_i$ ...
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1answer
332 views

Since the beta distribution is similar in form to the binomial, why do we need the beta distribution?

It appears that the binomial distribution is very similar in form to the beta distribution and that I can re-parametrize constants on either pdf to make them look the same. So, why do we need the beta ...
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0answers
76 views

Sufficient Statistic for Beta distribution

How can I show that the geometric mean $( \prod_{i=1}^{n} X_i )^{1/n}$ of a random sample of size $n$ from a distribution with pdf $f(x;\theta)=\theta x^{\theta-1},0<x<1,$, zero elsewhere, and ...
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1answer
85 views

The Conjugate Beta Prior proof

Hello. I'm having a problem with trying to figure out this proof that shows the beta distribution is conjugate to the binomial distribution (picture attached). I understand it until the third row, ...
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2answers
425 views

Calculate the confidence interval for the mean of a beta distribution

Consider a beta distribution for a given set of ratings in [0,1]. After having calculated the mean: $$ \mu = \frac{\alpha}{\alpha+\beta} $$ Is there a way to provide a confidence interval around ...
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1answer
38 views

Probability distribution satisfying constraints?

Reposted from Math.SE: Continuing from this question. Given two random variables $X$ and $Y$ where $X \sim \operatorname{Beta}(a, b)$ and $Y \sim \operatorname{Beta}(c, d)$, I'm looking for a random ...
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0answers
69 views

Computing Confidence in A/B testing

First of all, I'm fairly new to Decision Theory and my question might be rather too simple for the experts. I am having some issues in computing confidence for A/B Testing. I will first explain the ...
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1answer
93 views

Beta distribution and beta binomial distribution

What is the difference or relation between beta distribution, beta binomial distribution and binomial distribution?
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1answer
133 views

UMP of a Beta($\theta,1$) distribution

I need to find the UMP of a random sample of a BETA$(\theta,1)$ distribution. I know that the pdf of this problem is $$f(x;\theta)=\theta x^{\theta-1}=\theta e^{(\theta-1)\log{x}}$$ After some ...
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1answer
337 views

Approximation for Beta distribution when alpha is less than 10

I know that we can approximate Beta distribution to Normal distribution when the values of alpha and beta are large numbers. In my problem alpha lies between 1 and 10, beta is always greater than ...
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80 views

Model multilevel proportion data

Suppose that one has data on a proportion $P$ measured on a continuous scale. Further suppose that this data has a grouped structure -- some proportions are clustered according to a certain variable ...
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225 views

Beta distribution fitting in Scipy

According to Wikipedia the beta probability distribution has two shape parameters: $\alpha$ and $\beta$. When I call scipy.stats.beta.fit(x) in Python, where ...
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4answers
960 views

Does the beta distribution have a conjugate prior?

I know that the beta distribution is conjugate to the binomial. But what is the conjugate prior of the beta? Thank you.
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1answer
93 views

Posterior probability - change in Beta hyperparameters

Can you explain, how does $\text{B}(\alpha, \beta)$ transfrom to $\text{B}(s+\alpha, f+\beta)$ in the following equation? $$ \begin{align*} p(\left. q=x \right| s,f) &= {{{s+f \choose s} ...
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0answers
71 views

Degenerate cases when using naive bayes to infer a beta distributed variable

I'm trying to predict the distribution of a variable that I expect to be beta distributed, conditional on some associated text. I've measured the beta distributions conditioned on each term ...
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1answer
422 views

How do I choose parameters for my beta prior?

Suppose today I'm going to flip a coin. I believe that 9 of 10 flips will come up heads. I flip the coin and 8 of 10 are heads. Is my distribution of belief beta(9+8, 1+2) beta(1+9+8, 1+1+2) ...
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1answer
888 views

How to interpret the coefficients from a beta regression?

I have some data that is bounded between 0 and 1. I have used the betareg package in R to fit a regression model with the bounded data as the dependent variable. My ...
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1answer
86 views

How to compute lower edge of a credible interval for a beta distribution in python?

Suppose I flip a coin 584,369 times and observe 5,257 heads and 579,112 tails. I wish to know the lower edge of the 90% credible interval for the probability that the next flip will come up heads. I ...
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0answers
513 views

Proportion data: - beta regression or logit transformed OLS regression?

I have proportion data (percentage viewership of TV programs) that i'd like to model as a function of various demographics (age, sex etc.) and time (year). After surveying options for appropriate ...
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0answers
185 views

How to interpret results of GLM with a beta distribution in R?

I'm currently working on a project where my model is a GLM with a beta distribution. The dependent variable is bimodal. I've done this before, in Stata, but I'm having some difficulty interpreting ...
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1answer
124 views

Calculating Kurtosis with Beta distribution in R

I am working on an assignment question in R. The problem I am having is to calculate the Kurtosis using Beta distribution. So far I am able to get the kurtosis value of ...
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1answer
62 views

How can I tell if modelling/testing with Binomial/Beta is correct?

My standard disclaimer: I'm a programmer, not a stats guy, mostly wanting to understand statistical tests for optimizing web apps. Let's say I want to measure monetization rate of users. "How many ...
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2answers
212 views

Update rule for beta distribution with fixed K/confidence/sample size

Normally you have a beta distribution with shape parameters $a$ and $b$. The mean of this distribution is $a / (a + b)$ and the sample size, or the confidence (or K) is $a + b$. Now, if you do some ...
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1answer
75 views

Analytical approximation of probability of one beta-distributed var being greater than another?

The answer to What is the probability P(X > Y) given X ~ Be(a1, b1), and Y ~ Be(a2, b2), and X and Y are independent? provides an analytical solution for this, but is there a less computationally ...
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1answer
162 views

Calculate the probability that the difference between two populations is >= d

I'm a programmer, not a mathematician. I have tried to use real math terms and notation here, but I may be misusing them. I am doing split-testing, and I want a test to compare different ...
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1answer
58 views

Is it possible to find out how unlikely a given $\mathrm{Beta}(\alpha,\beta) – \mathrm{Beta}(\alpha’,\beta’)$ is?

Let $X_i$ be the distance between two nodes in a graph. $X_i \sim \mathrm{NB}(r,p)$ where $p \sim \mathrm{Beta}(\alpha, \beta)$. After the posterior hyperparameters are obtained, ...
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1answer
536 views

Dealing with regression of unusually bounded response variable

I am attempting to model a response variable that is theoretically bounded between -225 and +225. The variable is the total score that subjects got when playing a game. Although theoretically it is ...
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4answers
953 views

Beta regression of proportion data including 1 and 0

I am trying to produce a model for which I have a response variable which is a proportion between 0 and 1, this includes quite a few 0s and 1s but also many values in between. I am thinking about ...
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5answers
12k views

What is the intuition behind beta distribution?

Disclaimer: I'm not a statistician but a software engineer. Most of my knowledge in statistics comes from self-education, thus I still have many gaps in understanding concepts that may seem trivial ...
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1answer
145 views

Bayesian updating - which distribution to use

I'd like to use Bayesian updating to form price expectations to be used in another model. I'm very new to this area, so your help would be highly appreciated. I'm not sure which distribution to use ...
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1answer
106 views

Variance of compound distributions

I am stuck at solving analytically the variance (or standard deviation) of a combination of poisson distribution and Beta-Distribution (or more exactly, PERT distribution). The background is that for ...
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1answer
156 views

Is such transformed beta a known distribution?

I have a distribution $Y \sim 1/(1-Beta(\alpha,\beta))$. I would like to understand its properties. I was able to write down its density function, but I was not able to integrate it to get its mean, ...
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2answers
651 views

How can I model a proportion with BUGS/JAGS/STAN?

I am trying to build a model where the response is a proportion (it is actually the share of votes a party gets in constituencies). Its distribution is not normal, so I decided to model it with a beta ...
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0answers
293 views

What do I do if my predicted values are out of the dependent variable range?

I have built a beta regression model with log link for predicting adherence. My dependent variable's range is 0 to 1.When I used a test set to calculate the predicted values with the parameter ...
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1answer
460 views

Beta distribution from mean and quantile

Suppose I'm given the mean and one quantile (e.g. the 20% quantile) of a random variable $x$, and I want to find the parameters $\alpha$ and $\beta$ of a Beta distribution that has the same mean and ...