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

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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
18 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
22 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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0answers
18 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
35 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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35 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 ...
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1answer
109 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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51 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
100 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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10 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
50 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 ...
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237 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 ...
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2answers
205 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
71 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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38 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 ...
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1answer
66 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
63 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 ...
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1answer
88 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 ...
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1answer
81 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 ...
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3answers
485 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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254 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
116 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 ...
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54 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 ...
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1answer
79 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
64 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 ...
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2answers
447 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 ...
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57 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 ...
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1answer
62 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 ...
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126 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!
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65 views

Drawing a random Sample on a Probability Distribution

Say I have multiple normal or beta distributions. So I have two questions. How do I Draw a random sample from a distribution? How do I compare determine which of my distributions has the largest ...
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1answer
90 views

Find parameters $\alpha$ and $\beta$ of a beta distribution, if I have one quantile and the mean [duplicate]

Suppose I'm given the mean and one quantile (e.g. the 95% 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 ...
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31 views

modeling error when estimating the parameters of the beta distribution

After reading Basketball Beta and Bayes, I started to think about parameter estimation with observational error. If you are counting the number of successful and failed free-throws how can you ...
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34 views

Issue with Beta distribution

Question 1: When we merge two beta distribution, how do we arrive at the posterior parameter values? Which is the right formula and why? In one of my earlier queries, Henry mentioned Option 2 as ...
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126 views

Appropriate GLM when response variable is proportion, but not binomial

The response variable I'm dealing with is the proportion of a total area that is suitable habitat for a species of interest. So although the response variable is bounded between 0 and 1, my intuition ...
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2answers
96 views

Bayes factor for selecting between two beta-distributions

I have two beta-distributions: $H_1 = Beta(\alpha_1, \beta_1) $ and $H_2 = Beta(\alpha_2, \beta_2) $ (parameters are known), and I'd like to estimate whether a new sample $D$ rather comes from ...
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78 views

Outlier detection in beta distributions

Say I have a large sample of values in $[0,1]$. I would like to estimate the underlying $\text{Beta}(\alpha, \beta)$ distribution. The majority of the samples come from this assumed ...
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755 views

Why is this distribution uniform?

We are investigating Bayesian statistical testing, and come across an odd (to me atleast) phenomenon. Consider the following case: we are interested in measuring which population, A or B, has a ...
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1answer
63 views

Non-binomial posteriors for a binomial prior?

Let's assume we have a discrete binary random variable K (K=0 or K=1) for which the prior distribution is binomial. My understanding of Bayesian statistics tells me that regardless of the likelihood, ...
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1answer
85 views

Beta function approximation of delta function

I have modified the original question. Does beta distribution function $$f(x,\alpha) = \frac{[x^a(1-x)^b]^\alpha}{B(a\alpha+1,b\alpha+1)}$$ where $B$ is the beta function, approach delta function ...
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1answer
56 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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1answer
227 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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83 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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263 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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72 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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34 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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43 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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2answers
71 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, $p_i$, with $p_1+p_2+\dots+p_k=1$. Each probability has the same distribution. What would the distribution of a sum of probabilities be? For example, ...