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

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Error in R's pbeta function with log=TRUE. Why could it be? [on hold]

R's function pbeta is supposed to calculate the incomplete regularized Beta function. If the flag log=TRUE is passed as an ...
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1answer
77 views
+50

Probability distribution for a proportion based on (continuous) quantities

I have a problem related with probability distributions and parameter estimation, which comes from a real case. I would be very grateful if you could help me. Let us suppose that we have a continuous ...
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16 views

Calculate logarithm of Beta function for large alpha, beta in C++?

I want to calculate the logarithm of $\mathrm{B}_x(\alpha,\beta)$ for very large values of $\alpha,\beta$ (on the order of the thousands), where $\mathrm{B}_x(\alpha,\beta)$ is the incomplete Beta ...
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0answers
49 views

How to integrate products of beta distributions with large $\alpha$, $\beta$?

I have a product of Beta distributions, like ...
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1answer
26 views

beta-binomial distribution with R

I am studying an experiment of the kind: Let $n_{ij}$ be the number of fetuses, $X_{ij}$ the number of responses i.e. the number of fetuses with a malformation in the jth litter of the ith dose level ...
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0answers
11 views

The distribution of a product between a Lognormal and a Beta is …?

I have to random variables expressed as $1 \times 1000$ vectors. One of the vectors $B$ is Beta distributed while the other $L$ is lognormal distributed. Upon element-wise multiplication, I get vector ...
5
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1answer
48 views

Closed form for $\mathbb{E}[\ln (1-p)]$, for $p \sim Beta(\alpha, \beta)$

We know that if $p \sim Beta(\alpha, \beta)$, then $$ \mathbb{E}[\ln p] = \psi(\alpha) - \psi(\alpha + \beta) $$ where $\psi(.)$ is the Digamma function. Is there an easy form for $ \mathbb{E}[\ln ...
2
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1answer
22 views

Why do we make a F-Test rather than a Beta-Test in ANOVAs?

When one performs an ANOVA, (s)he always end up calculating the observed F-ratio and comparing it to the appropriate F-distribution. From this post, I discovered that the coefficient of correlation ...
2
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2answers
145 views

How to add noise to a random variable whose range is the unit interval? [closed]

I have a list of values sampled from a beta distribution that therefore lie in the interval [0,1]. I would like to add (e.g. Gaussian) noise to these values, but of course there is the problem of the ...
2
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0answers
20 views

Hypothesis testing on data from a continuous proportion beta distribution

I am interested in identifying factors that influence the proportion of time each of my samples occupy one of two states (imagine it as ON vs OFF) throughout the course of one day. In a series of ...
5
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1answer
108 views

Distribution of the quotient of two gamma random variables with different rate parameters?

I have a question about how to derive the distribution of the quotient of two random gamma variables drawn from two different Gamma distributions with the same shape, but different rates. For example, ...
9
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1answer
268 views

If $X_1,X_2$ are independent beta then show $\sqrt{X_1X_2}$ is also beta

Here is a problem that came in a semester exam in our university few years back which I am struggling to solve. If $X_1,X_2$ are independent $\beta$ random variables with densities ...
3
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2answers
69 views

Mean and variance of a Beta distribution with $\alpha \ge 1$ or $\beta \ge 1$?

What conditions must satisfy the mean and variance of a Beta distribution so that the parameters $\alpha,\beta$ are not both less than 1?
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97 views

Can logistic regression be modified to predict a distribution, not just point-estimate? Other ways to learn a beta distribution from binary events?

Currently I'm using high dimensional logistic regression to predict the probability of a rare event. I use this probability for both ranking and for other calculations which need it to be ...
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0answers
7 views

Does the generalized beta distribution of McDonald and Xu constitute an exponential family?

Does the generalized beta distribution of McDonald and Xu, J. Econometrics 66 (1995) 133-152, constitute an exponential family? Can it be written in a way that makes this more obvious? Alternatively, ...
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2answers
100 views

Calculating marginal distribution via integration

Suppose that we have an IID random sample $\mathbf{x} = (x_1, \dots, x_n)$ from a given distribution with the following PDF: $$\theta (1 - e^{-x})^{\theta -1}e^{-x}, \, x > 0, \, \theta > 0$$ ...
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12 views

likelihood and gibbs for univariate UE model

This is the first time when i post something here. I would like to ask how can i compute the likelihood of the following model? i put only the product of the densities and that is it? I think the ...
2
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1answer
51 views

How to draw a random sample from a Generalized Beta distribution of the second kind

For microsimulations, I (i) want to estimate parameters of an empirical distribution and (ii) draw a random sample based on the estimations. My random variable $Y$ seems to follow a Generalized Beta ...
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12 views

Positive correlation coefficient, but negative Beta weights in multiple regression [duplicate]

I have a situation where IVs positively correlate with the DV, and the IVs also correlate with eachother. I do not explain how the beta weights are negative. No multicollinearity is detected, and the ...
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1answer
27 views

How do you work out the likelihood function for the beta geometric function?

I know the probability function for the beta distribution is $$p(x=k)=\frac{\prod_{i=1}^{k-1}(1-u+(i-1)\theta)}{\prod_{i=1}^{k}(1+(i-1)\theta)}$$ However I am unsure of how to derive the formula for ...
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1answer
42 views

Beta distribution vs beta binomial distribution: alpha and beta

I have been attempting to estimate alpha and beta from a beta binomial distribution given my data. There are R packages like VGAM to do this. I am wondering if there is a difference between estimating ...
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27 views

Incorporating population priors into MLE fits with few/limited samples

I am fitting Beta distributions to data resulting from each of many experiments using maximum likelihood. My goal is for each experiment, given iid data $y_{1:k}$, fit a Beta distribution, and then ...
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1answer
77 views

How to select hyperprior distribution for Beta distribution parameter?

I have a parameter $\theta$ whose value should lie between $(0,1)$. Therefore, I am assuming the prior distribution of $\theta$ to be a beta distribution with hyper-priors $\alpha$ and $\beta$ ie. ...
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63 views

How can I (numerically) approximate the quantile in a beta distribution in SQL?

I wrote some code in SAS that among other things, used the BETAINV function (or BETA.INV as it's called in Microsoft Excel) to calculate the quantile in a beta distribution corresponding to a random ...
2
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1answer
142 views

Is a gamma distribution bounded between 0 and 1 the same as a beta distribution? [closed]

After making the assumption that monetary losses could be well represented by a gamma distribution (Boland, 2007), mostly negatively skewed, and being interested in loss ratios (ie. lost value / total ...
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28 views

Show that $P(X \ge r ) = P (Y \le p)$ [duplicate]

Let $ X \sim \text{Bin}(n,p) $ and $ Y \sim \text{Beta}(r,n-r+1) $. Show , without integration by parts, that $P(X \ge r ) = P (Y \le p)$. From which point of view I answer this question.
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61 views

Calculate expected value from discrete beta distribution

I have a lookup table in 2 variables, $Z_l$ and $T_l$. So, $Z_l$ and $T_l$ are vectors with same length where $Z_l$ goes from 0 to 1 and $T_l$ varies between 300 and 2000. If you are curious, $Z_l$ ...
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1answer
107 views

Fitted Beta distribution always holds water. Can I force it not to?

I am trying to fit a beta distribution to election forecast data. The ultimate purpose is determining with what probability the election will be decided by one vote (more on this here). My data is as ...
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11 views

Performing OLS with gamma transformation

In some specific areas it is common to perform OLS regresion with beta distribution transformation. The α and b parameters are calculated by the sample's μ and σ^2. While the transformed dependent ...
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1answer
71 views

Tail bounds for Beta distribution

Say $X\sim\mathrm{Beta}(\alpha,\beta)$. Are there any "nice" closed form upper bounds for the tail probability $P(X\geq\epsilon)$, that are reasonably tight when $\beta$ is large? By "nice" I mean ...
3
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2answers
464 views

Proportion data - beta distribution v. GLM with binomial distribution and logit link

I have a fisheries dataset for which I have calculated value for each grid cell on a map. The value is the proportion of the total fishing sets in that cell for each month/year. So, I have values ...
2
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2answers
221 views

Problem interpreting the Beta distribution

On p38 of Lee and Wagenmakers (2012) "Bayesian Cognitive Modeling: A Practical Course" the following passage appears: "One of the nice properties of using the θ ~ Beta (α,β) prior distribution ...
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1answer
103 views

Kernel density estimation on bounded support

I was looking for some way to deal with boundary bias of kde in case of unit interval. One example is an usage of Chen estimators (or Beta estimators; an example might be seen here: ...
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72 views

Regression Modeling with Upper and Lower Bounds on target distribution

I am trying to run a simple regression model between a couple of variables, one of which is bound between values of (.25 - .75). This will be my target variable. I understand the beta distribution can ...
2
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1answer
97 views

Model averaging when linear and quadratic effects are modeled in a global model

I am trying to derived estimates of model-averaged parameter effects on a fairly complicated set of models using an information-theoretic approach. I have several models that investigate continuous ...
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14 views

Estimating the loss between two Beta distributions

Suppose I have two coins, $A, B$ that each come up heads with probability $p_A, p_B$. Starting with a uniform prior on the values of $p_A, p_B$, and seeing data $s_A$ heads out of $N_A$ attempts, ...
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12 views

Bounds on binary event estimation

I would like to paint an objective picture of some binary outcome. Now I have data like this: 1085x yes, 1704x no. The percentage of the positive outcome is 40.72%, but I want to give an estimation ...
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2answers
80 views

Beta regression

I have a data set where the response variable Y is a rate between 0 and 1, where the histogram of Y is bimodal. So I feel the linear regression is not suitable.s I have been reading papers about ...
2
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1answer
99 views

Recursively updating the parameter of a Beta function in a bayesian way?

I ask, because it is very hard to find information regarding the beta distribution and the bayesian inference, where the beta distri is NOT the prior. My goal is to identify or to improve the two ...
0
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1answer
98 views

Create a threshold for binary classification problem based on distribution of criterion

I created a criterion for my financial data-set for classify data to two classes for other processing (like neural network binary classificatio). After calculating ...
2
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3answers
528 views

When is beta distribution bell-shaped or concave?

Is there some restriction to parameters $( \alpha , \beta)$ that makes the beta distribution concave down? Bell-shaped like e.g. a normal? For example, the cases in purple and black, but not the red ...
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342 views

Interpretation of Zero-One inflated Beta Regression with R (GAMLSS)

I am not that familiar with the interpretation of a beta regression with the r-package GAMLSS. Papers and package manuals didn`t help me. I modeled a Zero-One inflated Beta Regression. The ...
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1answer
133 views

Determining beta distribution parameters $\alpha$ and $\beta$ from two arbitrary points

Suppose I have two points $(p_1,x_1)$ and $(p_2,x_2)$ where $p_i$ is a probability on the beta CDF and $x_i$ is a value on that same CDF. How would I go about determining the beta distribution shape ...
0
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1answer
58 views

PDF not matching histogram of synthetic ratios of independent beta

The PDF of the ratios of independent beta variables is described in http://www.tandfonline.com/doi/abs/10.1080/03610920008832632#.U9J02vldUcC To explore the implications, i created an implementation ...
3
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1answer
84 views

sum and product rules of probability

I am reading Bishop's Pattern Recognition and Machine Learning. In page 73, chapter 2.1. I can't understand the formula 2.19 : $$p(x=1|\mathcal{D})=\int_0^1 p(x=1|\mu)p(\mu|\mathcal{D})\text{d}\mu ...
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1answer
84 views

Sum of Beta-Bernoulli variables

Assume you have $x_i \sim \operatorname{Bernoulli}(p_i)$ with $p_i \sim \operatorname{Beta}(\alpha,\beta)$. I am exploring $Z=X_1+ \dots +X_n$ According to this page, it is $Z \sim ...
5
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2answers
510 views

Is the beta distribution really better than the normal distribution for testing the difference of two proportions?

I'm working at an online agency, where we run a lot of AB testing in order to test differences in proportion between two groups (test vs. control). Standard practice in the industry for testing ...
4
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59 views

Approximate a product of Beta PDFs with another Beta PDF

The PDF of the generalized Beta distribution in the interval $[A,B]$ is defined as: $$f(x) = \frac{(x-A)^{\alpha-1}(B-x)^{\beta-1}}{(B-A)^{\alpha+\beta-1}\mathrm{B}(\alpha,\beta)}$$ for ...
2
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1answer
73 views

$\alpha,\beta\ge 1$ in a Beta distribution. What does it imply for the mean and variance?

The Beta distribution has the PDF: $$f\left(x\right)=\frac{x^{\alpha-1}\left(1-x\right)^{\beta-1}}{\mathrm{B}\left(\alpha,\beta\right)}$$ for $0<x<1$, and $f(x)=0$ otherwise. The parameters ...
5
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1answer
130 views

Product of Gamma by Beta rv

If $X$ has a beta distribution $ \beta(\alpha,b)$, $Y$ has a gamma distribution $\Gamma (K,\theta)$ and $X$ is independent of $Y$. What is the distribution of the product $P=XY$ . Thanks!