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

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3
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56 views

Beta as distribution of proportions (or as continous Binomial)

Beta distribution is related to binomial being also the distribution for order statistics. Probability mass function of binomial distribution is $$ f(k) = {n \choose k} p^k (1-p) ^{n-k} \tag{1} $$ ...
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0answers
15 views

Test for Equality of Parameters in Beta-Binomial Distribution

With binomially distributed data, it's straightforward to test the null hypothesis of equiprobable responses, $H_0: p=0.5$, but say you want to test the analogue in a Beta-Binomial model fit to ...
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1answer
64 views

How to determine posterior distribution of the parameter in a binomial

Assuming that I performed n iid tests, and the total number of test is n which is a fixed value, and the observaton of 1 which corresponding to successful results is X observations yeild with ...
5
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1answer
81 views

Distribution of differences in beta-distribution

I want to get an analytic solution to the difference of the highest and second highest of a beta distribution. More simply, I have some datapoints on which I assume a beta-distribution. Analytically ...
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0answers
17 views

Is it valid to say higher Beta values are more significant in a regression model

I wanted to know if the above statement is always valid. For example in a simple linear or binomial regression model do variables with higher beta coefficients always have higher significant values ...
0
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0answers
29 views

Survival Analysis - Improbable Exp(B)?

I'm currently conducting a survival analysis on my dataset. I have data on adoption of a new service and am using a Cox Proportional Hazard Model in order to account for right-censored observations. ...
0
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0answers
48 views

Mixture of beta distrubutions

I have data; one column and 310 rows. When I plot the histogram, it has two peaks; see the figure. I would like to find appropriate distribution that fits the data. I tried to mixtools in R, but it ...
0
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1answer
27 views

Independent and dependent gives the same results?

Is there any situations where considering two random variables independently and dependently leads to same computational result ? Is there a reason why this might happen ? My specific problem deals ...
3
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1answer
30 views

Difference between standard beta and unstandard beta distributions?

What is the difference between standard beta and unstandard beta distributions? How to understand in an article if it is not described if it is standard or not?
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0answers
38 views

Estimating beta parameters in truncated beta-binomial distribution

I'm sampling a bunch of probabilities, $\theta_i \sim Beta(a,b)$, from a common beta distribution, and then using each $\theta_i$ to sample a value $x_i$ out of $N_i$ possibilities. However, I am only ...
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0answers
24 views

Let X_1,…,X_n be a random sample from the Beta disribution with parameters a = θ and b = 1 [closed]

I need to find the UMVUE for 1/θ but need some help. I don't know how to find a complete and sufficient statistic to start so I can't go much further. Thank you.
6
votes
3answers
128 views

Distribution of $XY$ if $X \sim$ Beta$(1,K-1)$ and $Y \sim$ chi-squared with $2K$ degrees

Suppose that $X$ has the beta distribution Beta$(1,K-1)$ and $Y$ follows a chi-squared with $2K$ degrees. In addition, we assume that $X$ and $Y$ are independent. What is the distribution of the ...
4
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1answer
34 views

Ancillary statistics:Beta distribution is free of $\beta$?

I am reading Robert V. Hogg Introduction to Mathematical Statistics 6th Version page 409, second paragraph. $X_1, X_2$ is a random sample from a Gamma $\text{G}(\alpha,\beta)$ distribution with ...
8
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0answers
86 views

Jaynes' $A_p$ distribution

In Jaynes' book "Probability Theory: The Logic of Science", he has a chapter (Ch 18) entitled "The $A_p$ distribution and rule of succession" in which he introduces the idea of $A_p$ distribution; ...
7
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3answers
366 views

Understanding the Beta conjugate prior in Bayesian inference about a frequency

Following is an excerpt from Bolstad's Introduction to Bayesian Statistics. For all you experts out there, this might be trivial but I don't understand how the author concludes that we don't have ...
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0answers
16 views

How Can I Combine Multinomial Data from Survey with Two Parameter Univariate Distribution

I have survey data, $X$ that measures a variable on a 1-5 Likert type-scale. I have a second variable $Z$ which, given a suitable parametric assumption, I can identify the mean and the variance but ...
0
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1answer
68 views

How can I improve this glm and do I need to dummy code?

I have percentage disease data taken from leaves of wheat in a disease trial which were artificially inoculated with isolates of disease from different source plants. The basic question is, are ...
0
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1answer
84 views

Fit a Beta Regression model to a U-shaped Dependent Variable

I have a dependent variable, y, which appears to show a U-Shaped pattern. I want to prove that a U-shape is the most likely model than any other model type. Since my y variable is percentages, it ...
3
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0answers
30 views

Expectation of convex function of a Beta random variable

Suppose I have two Beta random variables $$ X \sim \text{Beta}(a, b), \\ Y \sim \text{Beta}(ca, cb), $$ with $c > 1$. They both have same mean $\tfrac{a}{a+b}$, but $Y$ is more "peaky" than $X$. My ...
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0answers
41 views

Beta prior on (a,b)

Is it possible to rescale a beta prior to range from, say, $(0.5,1.0)$? For example, say that your likelihood function for some parameter $p$ is binomial and you know that $p \in (0.5,1.0)$ due to ...
2
votes
1answer
31 views

Transformation of variables in Beta distribution of first kind

If $X$ and $Y$ follow Beta distribution, with parameters $m$ and $n$, of first kind and are independent random variables. Then what is the distribution of $(X+Y)$? I took $U=X+Y$ and $V=Y$ Then I ...
3
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2answers
90 views

What is the equivalent of Student's t-distribution on an interval?

I have been using Student's t-distribution as a proxy for the Gaussian distribution estimated from a limited number of points in order to calculate alpha-intervals (for instance 95% confidence ...
0
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0answers
14 views

Transforming a beta distribution to non-log linear space

I'm interested in adapting methods that use support vector regression on non-log linear data to work with data that are beta distributed. I want to know what approaches exist to convert beta values to ...
3
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0answers
46 views

Fitting datas, lognormal and beta distribution, interpretations

I've been given some data that should come from a lognormal distribution. I've got some issues concerning the fitting, here's what I did. ...
0
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1answer
79 views

Convert probabilities of “binomial events” into beta distribution for binomial parameter (theta)

I have three events that essentially arise from a binomial distribution with k=2, i.e., X~Binomial(theta,n=2). Given some model and data I obtained a conditional (pos distribution for a particular ...
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2answers
88 views

Beta distribution GLM with categorical independents and proportional response

My data is percentage disease data of different varieties of plants that had been inoculated with disease from several different sources. having conducted two-way ANOVA in SPSS (using the log10+1 of ...
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3answers
268 views

Generating Beta distributions with Uniform generators

I can generate as many samples from one or more uniform distribution (0,1) as I wish. How can I use this to generate a beta distribution ?
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1answer
29 views

Distribution of partially observable binominal parameter

I suspect this is a textbook question but I don't seem to have the right textbook. Anyway I am trying to estimate probability of coin landing on heads, p, by repeatedly flipping it N times, i.e., ...
2
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1answer
50 views

On a possible generalization of the Beta distribution

Imagine that Alice is flipping a coin with unknown bias $\theta$ and reporting the results to Bob, who is conducting Bayesian inference. If Bob begins with a uniform prior, then his posterior ...
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1answer
53 views

Inferential statistics for vector of percentages

I'm getting confused by this and was wondering if someone can enlighten me: I have a random sample consisting of 50 percentages. Each percentage can take on any value between 0% and 100% inclusive ...
2
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0answers
31 views

Distribution over the product of three, or n, independent Beta random variables

This is a re-post of a question on the Mathematica stack exchange, as per the advice of another user (see here). I am pursuing a computational solution there, but thought it might be worth looking for ...
0
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0answers
21 views

Scale dataset in R [duplicate]

I have 528 observed temperature data. The values of the data range $[2, 53]$. I have to scale the data to make it range between 0 and 1 to fit a beta distribution to find whether the beta distribution ...
0
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1answer
43 views

How do I get the alpha and beta of a non-central beta distribution from mean and variance in R?

I need to fit a beta-distribution a real data, with a mean of 0 and a standard deviation of 0.17. I have read that this is possible by using the non-central beta distribution, and I would wlike to ...
0
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1answer
67 views

Probability distribution for a binomial proportion 'derived' from serially dependent data

Consider the following type of data: This is data from a single-case experiment: an experiment in which one entity (i.e. one person) is observed repeatedly over time (cf. measurement times 1 to ...
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0answers
107 views

Zero-and-one inflated beta regression vs. binomial GLMM?

I appreciate some help with deciding whether I should (and how to) construct a zero-and-one-inflated beta regression model. I want to use R to test the hypothesis that there is a ...
0
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2answers
94 views

Median of ratio of independent variates with Beta distributions

Let $X, Y$ be independent random variables where $X \sim Beta(\alpha_1,\beta_1)$, $Y \sim Beta(\alpha_2,\beta_2)$, and $Z = X/Y$. Recall $X, Y$ are supported on $(0,1)$, so $z > 0$. I've ...
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1answer
60 views

Calculating parameters for a mixture of beta distributions

I have two beta distributions with known parameters: ...
2
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1answer
105 views

Credible set for beta distribution

How can I approximate beta distribution $\alpha=x+1$ and $\beta = 14-x$ to normal distribution? Or, could you please tell me how to calculate HPD credible set for beta distribution?
3
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1answer
69 views

Estimating the parameters of a Beta distribution using the sample average and standard deviation

This is a simple question, but I just want to be sure. Imagine that we have a sample of $n$ data $\{x_1, \dots, x_n\}$ and that we want to fit them to a Beta distribution. Imagine that we have ...
4
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1answer
172 views

Approximating the distribution of a linear combination of beta-distributed independent random variables

This question is related with these other two questions in Cross Validated, which has been already answered: Approximate the distribution of the sum of ind. Beta r.v Central limit theorem when the ...
3
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0answers
149 views

Hyperprior Noninformative Beta Binomial Model

I've been working through Gelman's Bayesian Data Analysis 3 text and have been trying to understand one of the hierarchical models revolving around rat tumors (Chapter 5). He uses a binomial model ...
7
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2answers
222 views

Order statistic for beta distribution

Let $x_1,\dots,x_n$ be i.i.d. draws from $Beta\left(\frac{k}2,\frac{k-p-1}{2}\right)$. How are the minimum and maximum order statistics distributed, respectively? I would greatly appreciate a ...
0
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0answers
17 views

What class of functions can be covered by beta functions in Bayesian statistics?

I was thinking about Bayesian statistics, and one thought bothered me: In Bayesian statistics, we assume that the pdf $p(x)$ can be described as: $p(x)=\int f(x|\theta)g(\theta)d\theta$ usually ...
0
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0answers
27 views

gnet solution path plot in spike slab regression

in spike slab regression in R, please someone answer me that how we comment the plot of gnet solution path below? I know that the blue ones represent the zero and red ones for nonzero but what does it ...
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0answers
20 views

spike slab with R

in spike slab regresson, how do we understand the beta coefficients signicant in output in R? I mean, R gets "bma" and "gnet" solutions like below, these coefficients are the significant ones? So it ...
0
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0answers
24 views

analytically finding the dispersion of beta distribution in multilevel bayesian model

I want to create a multilevel bayesian model of the format depicted in the in figure below. I am examining # of conversions (out of total number of exposures) in multiple subgroups. The conversion ...
0
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0answers
60 views

Confidence interval of the mean for a beta distribution when alpha and beta are estimated [duplicate]

I have elementary knowledge in statistics. I'm trying to estimate the confidence interval for mean of a beta distribution as specified in this article using log likelihood estimation given alpha, beta ...
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1answer
27 views

Scaling behavior of the width of a distribution

I'm considering the following distribution on the interval $[-1,1]$: $$p(x)=\frac{1}{N}(1-x)^{n-p}(1+x)^p$$ where $N$ is a normalization factor while $n, p \in \mathbb N $ and $2\leq n$ and $ 1\leq ...
3
votes
1answer
95 views

Bivariate distribution: beta and binomial

Consider a pair of RVs $X$ and $Y$, with the following conditional distributions: $$X | Y=y \sim Binom(L, y)$$ $$Y | X=x \sim Beta(\alpha + x, \nu)$$ where $L$, $\alpha$, and $\nu$; are all ...
6
votes
1answer
263 views

Logarithm of incomplete Beta function for large $\alpha,\beta$

R's function pbeta is supposed to calculate the incomplete regularized Beta function. If the flag log=TRUE is passed as an ...