# Tagged Questions

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

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### Maximum entropy distribution of a proportion with known mean and variance? Is it a beta?

Given a proportion and its standard error, what distributional assumption minimizes assumptions/maximizes entropy? Is it the beta (and can I use the method of moments to estimate its parameters)? Or ...
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### general transform methods to generate random values fro beta distribution [closed]

(a)write r function to first generate Exp(1) random values and to then use an appropriate transformation to generate values from Beta(a,b)distribution. (b) Run your function to generate 10000 values ...
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### Nonlinear transformation using the beta distribution

I'm trying to estimate the following equation (abstracted from this paper) in Matlab: $y_i=a+b\frac{(x_i-min(x))^{(c-1)}(max(x)-x_i)^{d-1}}{B(c,d)(max(x)-min(x))^{c+d-1}}+\epsilon_i$ where $B(c,d)$ ...
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At a critical stage in the development of a new aeroplane, a decision must be taken to continue or to abandon the project. The financial viability of the project can be measured by a parameter $\... 0answers 33 views ### Closed-form equation for$\int_{0.5}^{1} Beta(\alpha,\beta)$? I don't know if this question is too trivial for you guys, it is not for me though... Is there a closed-form equation for$b = \int_{0.5}^{1} Beta(\alpha,\beta)$? $$Beta = \frac{x^{\alpha-1}(1-x)^{\... 0answers 63 views ### Distribution of the ratio of two shifted generalized gamma random variable X \sim \mathrm{GG}\left(p,d,\theta_{1},\mu\right) where p is power, d is shape, \theta_1 is scale and \mu is location parameter. Also Consider Y \sim \mathrm{GG}\left(p,d,\theta_{2},\mu\... 1answer 37 views ### Regression (Beta weights and correlation) I have used regression to explain a dependent variable with a number of independent variables. I expected independent variables which have higher correlations with the dependent variable to have ... 1answer 24 views ### If X is Beta distributed, what is distribution of Y: Y=1 for X>0.5 and Y=0 otherwise Consider random variable X \sim \mathrm{Beta}(\alpha,\beta) What is the distribution of Y defined by Y\in \{0,1\}, Y=1 if X>0.5 and Y=0 otherwise. 0answers 16 views ### Bayesian A/B/C testing I built a Bayesian A/B testing tool - i.e. one which models A and B having posteriors Beta(\alpha_i, \beta_i) where \alpha_i, \beta_i are updated every iteration. After T iterations, I compare ... 0answers 24 views ### Large sample distribution arising from a beta distribution Let X_1,X_2,... be a sequence of i.i.d. random variables having p.d.f as, f(x)=\frac{1}{B(6,4)}x^5(1-x)^3,0<x<1. Let Y_i=\frac{X_i}{1-X_i} and U_n=\frac{1}{n}\sum Y_i.We have to find,... 1answer 72 views ### Show that \frac{X}{X+Y}\sim Beta(\alpha,\beta) [duplicate] Let IG denote Inverse-Gamma distribution Inverse-Gamma. If X\sim IG(\alpha,1) and Y\sim IG(\beta,1). Show that \frac{X}{X+Y}\sim Beta(\alpha,\beta) I tried with jacobian transformation ... 1answer 26 views ### How to proper evaluate the PDF of a Beta Distribution? On page 40 of "Think Bayes - Bayesian Statistics Made Simple", Allen evaluates the PDF of the Beta distribution as ... 0answers 60 views ### seeking proof of a necessary condition of a beta inequality Assume we have two Bernoulli trials with success probability c_1 and c_2 (c_1>c_2 and c_1,c_2\in(0,1)), respectively. Now we use two beta distributed random variables e_1\sim Beta(\alpha_1,... 0answers 42 views ### Error Observed in Beta Regression Modelling I am using beta regression to model fulfillment ratio of a store (orders delivered/orders placed), which is between 0 and 1. I am using betareg package in RStudio to run this analysis. I have 24 ... 0answers 6 views ### Difference Beta on b-path depending on independent variable (all else being equal) I hope you can help me with 2 questions: 1. Difference in B-path value I have run a simple mediation with one independent variable on two independent variables with a mediator and a covariate. Here ... 0answers 35 views ### Bayesian updating of scaled beta distribution I would like to know how to link a scaled beta distribution to its non scaled beta distribution. For some context: I have a model where I want to estimate the proportion (\pi) of people belonging ... 3answers 50 views ### Why can I combine gamma and factorial coefficients for a beta conjugate posterior A commenter reminds me to be clearer. In a Bayesian context, the product of a binomial likelihood and a beta prior probability is$$\left( {\begin{array}{*{20}{c}}n\\x\end{array}} \right)p_{}^x{(1 -... 0answers 35 views ### how does the beta function make the total probability of Dirichlet distribution integrate to 1? [duplicate] the Dirichlet distribution $$Dir(\boldsymbol\mu|\boldsymbol\alpha)=\frac{1}{B(\boldsymbol\alpha)}\prod_K\mu_k^{\alpha_k-1}$$ How is the normalization term$B(\boldsymbol\alpha)$calculated? or in ... 1answer 35 views ### picking out outliers from a GLM in R I recently fitted a beta distributed GLM using R (and the betareg package). as you can see the model is a reasonably decent fit, however there are a few outliers. i would like to run the model again ... 0answers 45 views ### Weibull Distribution v/s Beta Distribution I've recently fallen in love with the Weibull Distribution and have gotten a reason to see if there's a mapping of this distribution to an interval (0,1). After plotting the Beta Distribution against ... 1answer 58 views ### Beta approaching Binomial If we have a Beta likelihood and a binomial prior, we get a beta posterior. Can someone please explain why this approaches a binomial as$n\rightarrow\infty$. I plotted it and this appears to be the ... 0answers 18 views ### In SAS' PROC LOGISTIC why aren't the coefficients consistent with the odds ratios? Now before you point me to it, I've already read it: In PROC LOGISTIC why aren't the coefficients consistent with the odds ratios? Data used in this example accessed here as SPSS .sav; can be ... 0answers 31 views ### beta coefficient in Anova with R and XLStat I’m working with the software R and XLStat. I’ve conducted an one-way ANOVA (my categorical variable is 3 modal (1,2,3) and my ... 0answers 26 views ### Offset instead of percent data? In R I want to build a GLM explaining the fraction of a coral perimeter that is covered by different algae. I measured the perimeter of the coral (in cm, integer values) and fraction that is contacted ... 0answers 23 views ### Which distribution for percent composition data I want to test the effects of categorical enviromental parameters on the composition of sediments. I started to build a model using percent values of the (three) different compounds. However, I don't ... 0answers 9 views ### Why does the beta of a linear regression change when entering another step? [duplicate] I'm working with linear regressions in SPSS and am stumped by this issue. First, I'm entering my variables in three steps and get my beta value for Variable X in Model 3. Then, I'm adding another step ... 1answer 34 views ### Hyper parameters of Beta distribution Suppose$\theta \sim \beta(\alpha_1, \alpha_2)$and we believe that$E[\theta] = m$and$p(l < \theta < u) = 0.95$. Write a program that can solve for$\alpha_1$and$\alpha_2$in terms of$...
Let's say I have a beta distribution parametrized with $\mu, \phi$ such that given a random variable $X$ $$X\sim Beta(\mu,\phi),\quad \mu =\frac{a}{a+b}, \quad \phi = a+b$$ Now let a and b be ...