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

learn more… | top users | synonyms (1)

2
votes
1answer
27 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
votes
1answer
59 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 ...
1
vote
0answers
37 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
votes
2answers
80 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
votes
0answers
15 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
votes
0answers
12 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 ...
0
votes
0answers
5 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
votes
0answers
9 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
votes
0answers
57 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 ...
3
votes
1answer
51 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
117 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 ...
0
votes
1answer
192 views

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 ...
0
votes
0answers
31 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 ...
3
votes
0answers
58 views

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

I have a product of Beta distributions, like ...
1
vote
1answer
49 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 ...
0
votes
0answers
18 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
votes
1answer
53 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
votes
1answer
34 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
votes
2answers
183 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
votes
0answers
30 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
votes
1answer
223 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
votes
1answer
272 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
votes
2answers
78 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?
1
vote
0answers
116 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 ...
0
votes
0answers
10 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, ...
4
votes
2answers
104 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: $$\theta (1 - e^{-x})^{\theta -1}e^{-x}, \, x > 0, \, \theta > 0$$ ...
0
votes
0answers
13 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
votes
1answer
81 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 ...
0
votes
0answers
14 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 ...
1
vote
1answer
49 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 ...
0
votes
1answer
85 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 ...
2
votes
0answers
33 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 ...
1
vote
1answer
142 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. ...
1
vote
0answers
83 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
votes
1answer
183 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 ...
1
vote
0answers
29 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.
0
votes
0answers
81 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, $Z_l$ ...
1
vote
1answer
118 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 ...
0
votes
0answers
16 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 ...
1
vote
1answer
98 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
votes
2answers
740 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
votes
2answers
244 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 ...
2
votes
1answer
139 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: ...
1
vote
0answers
135 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
votes
1answer
123 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 ...
0
votes
0answers
19 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, ...
1
vote
0answers
14 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 ...
1
vote
2answers
98 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
votes
1answer
121 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
votes
1answer
110 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 ...