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

learn more… | top users | synonyms (1)

1
vote
2answers
25 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 ...
0
votes
2answers
37 views

Generating Beta distribution from Uniform distribution

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 ?
0
votes
1answer
17 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
votes
1answer
47 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 ...
1
vote
2answers
49 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
votes
0answers
28 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
votes
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
votes
1answer
30 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
votes
0answers
17 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 ...
0
votes
0answers
39 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
votes
2answers
72 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 ...
0
votes
1answer
31 views

Calculating parameters for a mixture of beta distributions

I have two beta distributions with known parameters: ...
2
votes
1answer
36 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?
2
votes
1answer
36 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
85 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
67 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
99 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
17 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
8 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
18 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
59 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
68 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
146 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
217 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
38 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
65 views

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

I have a product of Beta distributions, like ...
1
vote
1answer
71 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
20 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
58 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
44 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 ...
3
votes
2answers
235 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
34 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
303 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
275 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
86 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
123 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
23 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
112 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
100 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
115 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
38 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
194 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
115 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
216 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
84 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, $Z_l$ ...