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

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How to proper evaluate the PDF of a Beta Distribution?

On page 40 of "Think Bayes - Bayesian Statistics Made Simple", Allen evaluates the PDF of the Beta distribution as ...
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60 views

seeking proof of a necessary condition of a beta inequality

Assume we have two Bernoulli trials with success probability $c_1$ and $c_2$ ($c_1>c_2$ and $c_1,c_2\in(0,1)$), respectively. Now we use two beta distributed random variables $e_1\sim ...
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24 views

Error Observed in Beta Regression Modelling

I am using beta regression to model fulfillment ratio of a store (orders delivered/orders placed), which is between 0 and 1. I am using betareg package in RStudio to run this analysis. I have 24 ...
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5 views

Difference Beta on b-path depending on independent variable (all else being equal)

I hope you can help me with 2 questions: 1. Difference in B-path value I have run a simple mediation with one independent variable on two independent variables with a mediator and a covariate. Here ...
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32 views

Bayesian updating of scaled beta distribution

I would like to know how to link a scaled beta distribution to its non scaled beta distribution. For some context: I have a model where I want to estimate the proportion ($\pi$) of people belonging ...
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46 views

Why can I combine gamma and factorial coefficients for a beta conjugate posterior

A commenter reminds me to be clearer. In a Bayesian context, the product of a binomial likelihood and a beta prior probability is $$\left( {\begin{array}{*{20}{c}}n\\x\end{array}} \right)p_{}^x{(1 ...
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how does the beta function make the total probability of Dirichlet distribution integrate to 1? [duplicate]

the Dirichlet distribution $$Dir(\boldsymbol\mu|\boldsymbol\alpha)=\frac{1}{B(\boldsymbol\alpha)}\prod_K\mu_k^{\alpha_k-1}$$ How is the normalization term $B(\boldsymbol\alpha)$ calculated? or in ...
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20 views

picking out outliers from a GLM in R

I recently fitted a beta distributed GLM using R (and the betareg package). as you can see the model is a reasonably decent fit, however there are a few outliers. i would like to run the model again ...
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31 views

Weibull Distribution v/s Beta Distribution

I've recently fallen in love with the Weibull Distribution and have gotten a reason to see if there's a mapping of this distribution to an interval (0,1). After plotting the Beta Distribution against ...
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56 views

Beta approaching Binomial

If we have a Beta likelihood and a binomial prior, we get a beta posterior. Can someone please explain why this approaches a binomial as $n\rightarrow\infty$. I plotted it and this appears to be the ...
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13 views

In SAS' PROC LOGISTIC why aren't the coefficients consistent with the odds ratios?

Now before you point me to it, I've already read it: In PROC LOGISTIC why aren't the coefficients consistent with the odds ratios? Data used in this example accessed here as SPSS .sav; can be ...
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22 views

beta coefficient in Anova with R and XLStat

I’m working with the software R and XLStat. I’ve conducted an one-way ANOVA (my categorical variable is 3 modal (1,2,3) and my ...
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19 views

Offset instead of percent data?

In R I want to build a GLM explaining the fraction of a coral perimeter that is covered by different algae. I measured the perimeter of the coral (in cm, integer values) and fraction that is contacted ...
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15 views

Which distribution for percent composition data

I want to test the effects of categorical enviromental parameters on the composition of sediments. I started to build a model using percent values of the (three) different compounds. However, I don't ...
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9 views

Why does the beta of a linear regression change when entering another step? [duplicate]

I'm working with linear regressions in SPSS and am stumped by this issue. First, I'm entering my variables in three steps and get my beta value for Variable X in Model 3. Then, I'm adding another step ...
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34 views

Hyper parameters of Beta distribution

Suppose $\theta \sim \beta(\alpha_1, \alpha_2)$ and we believe that $E[\theta] = m$ and $p(l < \theta < u) = 0.95$. Write a program that can solve for $\alpha_1$ and $\alpha_2$ in terms ...
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54 views

Is there a Closed-form distribution for a Beta-Beta distribution?

Let's say I have a beta distribution parametrized with $\mu, \phi$ such that given a random variable $X$ $$X\sim Beta(\mu,\phi),\quad \mu =\frac{a}{a+b}, \quad \phi = a+b$$ Now let a and b be ...
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126 views

Probability density of sum of two beta random variables

Suppose that $X$ and $Y$ are independent and have beta distributions. $X$ has probability density function $g(x)=6x(1-x)$ for $ 0\leq x \leq 1$ and $Y$ has the probability density function ...
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14 views

Do betas from univariate GEE analyses equal correlation coefficients?

I have repeated data and need to determine the correlation coefficient between X and Y. Ive used GEE. Are the standardized parameter estimates from GEE (one variable X, predicting Y, repeated multiple ...
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40 views

Beta regression using GAMLSS: how to do post-hoc contrasts?

I have compliance rate data [0,1] from a mixed design study, which examines compliance rate over time for people receiving different types of incentives. I looked this up and thought that the beta ...
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44 views

What is the formula of Beta Coefficient in Logistic Regression?

I have my study about logistic regression, I have to make a software for the admission process of the school given that requirements result.. as the output to be passed or failed.. given the Logit = ...
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7 views

Change or shift the Beta distribution interval [duplicate]

I am trying to change the Beta distribution form the interval $[0,1]$ to $[0,2]$. Is that possible? I am just able to shift the distribution for example from the interval $[0,1]$ to $[3,4]$ with ...
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Why is rejection sampling with acceptance probability 2/3 for Beta(2,2) not slower than `rbeta(N,2,2)`?

I was trying to illustrate that rejection sampling is inefficient when an alternative approach is available that does not throw away samples. (This post obviously is a candidate for migration to SO, ...
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80 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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30 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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130 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 ...
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88 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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25 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 ...
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33 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. ...
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50 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 ...
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29 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 ...
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72 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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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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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.
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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 ...
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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 ...
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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; ...
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399 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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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 ...
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85 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 ...
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145 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 ...
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38 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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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 ...
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45 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 ...
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113 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 ...
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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 ...
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76 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. ...
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116 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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149 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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608 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 ?