# Tagged Questions

The beta distribution is used in beta regression, which can be very useful when the dependent variable has a floor or ceiling effect or is bounded.

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### Working out probability with alpha and beta

Working out probability with alpha and beta? Let's say in an experiment, the Null hypothesis is patients having Condition A. Alpha (type I error) is 0.05 and beta (type II error) is 0.15. If i have ...
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### How to interpret results of GLM with a beta distribution in R?

I'm currently working on a project where my model is a GLM with a beta distribution. The dependent variable is bimodal. I've done this before, in Stata, but I'm having some difficulty interpreting ...
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### Calculating Kurtosis with Beta distribution in R

I am working on an assignment question in R. The problem I am having is to calculate the Kurtosis using Beta distribution. So far I am able to get the kurtosis value of ...
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### How can I tell if modelling/testing with Binomial/Beta is correct?

My standard disclaimer: I'm a programmer, not a stats guy, mostly wanting to understand statistical tests for optimizing web apps. Let's say I want to measure monetization rate of users. "How many ...
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### How to - meta-analysis and forest plots using Beta correlation coefficients

Does anyone knows how to meta-analyse and create forest plots using beta-correlation coefficients?
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### Update rule for beta distribution with fixed K/confidence/sample size

Normally you have a beta distribution with shape parameters $a$ and $b$. The mean of this distribution is $a / (a + b)$ and the sample size, or the confidence (or K) is $a + b$. Now, if you do some ...
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### Analytical approximation of probability of one beta-distributed var being greater than another?

The answer to What is the probability P(X > Y) given X ~ Be(a1, b1), and Y ~ Be(a2, b2), and X and Y are independent? provides an analytical solution for this, but is there a less computationally ...
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### Calculate the probability that the difference between two populations is >= d

I'm a programmer, not a mathematician. I have tried to use real math terms and notation here, but I may be misusing them. I am doing split-testing, and I want a test to compare different ...
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### Draw conditioned beta distributed random variables

I am trying to draw a beta distributed random variable (recovery rate), conditioned on another beta distributed random variable (default rate). I have shape parameters $(\alpha= 0.6, \beta = 55.5)$ ...
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### Is a larger beta weight a better predictor than a high t-statistic?

Say there are two variables. Variable A has a higher beta weight than Variable B but variable V has a higher t-statistic than variable A. Can either of these measurements, standardized beta or ...
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### Is it possible to find out how unlikely a given Beta(alpha,beta) – Beta(alpha’,beta’) is?

X_i -> the distance between two nodes in a graph. X_i ~ NB(r,p) where p ~ Beta(alpha, beta). After the posterior hyperparameters are obtained, Beta(alpha,beta) – Beta(alpha’,beta’) could be found ...
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### Dealing with regression of unusually bounded response variable

I am attempting to model a response variable that is theoretically bounded between -225 and +225. The variable is the total score that subjects got when playing a game. Although theoretically it is ...
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### Beta regression of proportion data including 1 and 0

I am trying to produce a model for which I have a response variable which is a proportion between 0 and 1, this includes quite a few 0s and 1s but also many values in between. I am thinking about ...
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### What is intuition behind beta distribution?

Disclaimer: I'm not statistician but rather software engineer. Most of my knowledge in statistics comes from self-education, thus I still have many gaps in understanding concepts that may seem trivial ...
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### Estimate of parameter $\beta$

Suppose, I've a set of information, ...
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### Bayesian updating - which distribution to use

I'd like to use Bayesian updating to form price expectations to be used in another model. I'm very new to this area, so your help would be highly appreciated. I'm not sure which distribution to use ...
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### Maximum likelihood estimation for a beta distribution in R [closed]

I am trying to estimate the 2 parameters of a beta distribution by maximum likelihood method in R with the below code, but I keep getting an error while I am declaring the beta function in the code ...
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### Variance of compound distributions

I am stuck at solving analytically the variance (or standard deviation) of a combination of poisson distribution and Beta-Distribution (or more exactly, PERT distribution). The background is that for ...
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### Is such transformed beta a known distribution?

I have a distribution $Y \sim 1/(1-Beta(\alpha,\beta))$. I would like to understand its properties. I was able to write down its density function, but I was not able to integrate it to get its mean, ...
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### How can I model a proportion with BUGS/JAGS/STAN?

I am trying to build a model where the response is a proportion (it is actually the share of votes a party gets in constituencies). Its distribution is not normal, so I decided to model it with a beta ...
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### Z-scores and normalization in previously transformed data sets

I have two sets of data. The first is multivariate linear regression data consisting of betas and standard errors. It was log(e) transformed before the linear regression model was applied. The ...
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### What do I do if my predicted values are out of the dependent variable range?

I have built a beta regression model with log link for predicting adherence. My dependent variable's range is 0 to 1.When I used a test set to calculate the predicted values with the parameter ...
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### Beta distribution from mean and quantile

Suppose I'm given the mean and one quantile (e.g. the 20% 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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### Is it possible to interpret standardized beta coefficients for quantile regression?

Is it possible to interpret coefficients from a quantile regression on standardized data? Suppose I standardize the dependent variable $y$ and the independent variable $x$ (subtract the mean and ...
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### Iteration of the alpha parameter in a beta yields a beta?

I'd like to know whether starting from a Beta distribution and iterating it in the way described below, I will get a stationary (Beta) distribution again. More specifically this is the problem I am ...
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### If $Y \sim geometric(P)$ and $P \sim \mathcal B(2, 1)$ how to compute $E(Y)$ and marginal pmf of $Y$?

$$Y \sim Geometric(P)\\ P \sim \mathcal B(2, 1)$$ I'm trying to compute $E[Y]$ without finding marginal distribution of $Y$. I need some hints here. I also need to find the pmf of $Y$. My approach ...
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### Calculating Laplace–Stieltjes transform for general distributions

I am investigating exact and approximation methods to compute a Laplace–Stieltjes transform of various distributions. I know that it is easy for an exponential distribution, but I am confused for a ...
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### Real-life examples of common distributions

I am a grad student developing an interest for statistics. I like the material over-all, but I sometimes have a hard time thinking about applications to real life. Specifically, my question is about ...
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### Estimating the parameters of a beta distribution with zeroes and ones in the sample

I have a list of values in [0,1] that I want to fit to a Beta distribution in order to get the corresponding alpha parameter. I can't use a beta fitting function because my values might be 0's and ...
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### If $X \sim \mathrm{Gamma}(\alpha,1)$ and $Y \sim \mathrm{Gamma}(\beta,1)$, is $X/(X+Y) \sim \mathrm{Beta}(\alpha,\beta)$?

According to Wikipedia : $\mathrm{Beta}(\alpha,\beta) = \mathrm{Gamma}(\alpha,\theta) / (\mathrm{Gamma}(\alpha,\theta) + \mathrm{Gamma}(\beta,\theta))$ However, when I try to simulate this in R ...
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### Factor analysis and regression

I have a question about how to interpret a regression analysis I did following a factor analysis. I did prinicipal axis factoring (direct oblimin) I got a 3 factor solution. The three factors were ...
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### Variation on binomial experiment

Consider drawing stones from an urn with replacement. Suppose the urn contains a large number of stones, and each stone has a color, and the set of possible colors is large. Suppose $N$ stones are ...
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### Regression for an outcome (ratio) between 0 and 1

I am thinking of building a model predicting a ratio a/b, where a <= b, a > 0, b > 0. So, the ratio would be between 0 and 1. For independent variables, I have a continuous one and several 0/1 ...
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### Does my data come from a gamma or beta distribution?

I have data and I want to assertain whether it is beta or gamma distribution. Once I know what the distribution is, how do I find out what the parameters are? btw I am a complete novice
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### What does $\beta$ tell us in linear regression analysis?

I came across this note from a book - "..the correlation between the active and passive portfolios is greater when the $\beta$ of the active portfolio is higher.." The author runs regression of ...
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### What is the probability P(X > Y) given X ~ Be(a1, b1), and Y ~ Be(a2, b2), and X and Y are independent?

Given two independent variables with Beta distribution, $X \sim \text{Be}(a_1, b_1)$ and $Y \sim \text{Be}(a_2, b_2)$, how do you find the probability that the value of X is greater than the value of ...
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### Deriving posterior of Beta distribution

You test a classifier on a test set consisting of 10 iid items. The classifier makes 2 mistakes. Assume the true error rate is $x$. Let the prior be $x \sim Beta(\alpha, \beta)$. Derive the ...
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### Small Beta weight equals small structural coefficient

I have two predictors (X1 and X2) with large Beta's and large predictor-independent variable correlations (say it is like rs). In addition, I have another variable (X3; Beta=0.17; rs=0.18) which was ...
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### Converting Bs parameter estimates into Betas

I have unstandadized B coeff.s in my parameter estimates for ANOVA. How can I use Beta=B(SDx/SDy) to convert them into standardized B's (Beta's). Why doesn't SPSS do this for me, like it does in ...
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### Multi-level beta regression package for R?

I want to run multi-level beta regression with two levels (years nested within geographic pixels). I know about betareg, but as far as I know it doesn't have a multi-level option. Thanks.