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

learn more… | top users | synonyms (1)

3
votes
0answers
15 views

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 ...
0
votes
0answers
7 views

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 ...
1
vote
0answers
50 views

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 $B(c,d)$ ...
0
votes
0answers
37 views

Statistical Decision Problem and Prior Sensitivity

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 $\...
1
vote
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)^{\...
3
votes
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\...
1
vote
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 ...
0
votes
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.
0
votes
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 ...
1
vote
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,...
2
votes
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 ...
0
votes
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 ...
0
votes
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,...
0
votes
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 ...
0
votes
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 ...
1
vote
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 ...
2
votes
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 -...
5
votes
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 ...
0
votes
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 ...
2
votes
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 ...
2
votes
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 ...
0
votes
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 ...
0
votes
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 ...
0
votes
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 ...
2
votes
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 ...
0
votes
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 ...
2
votes
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 $...
3
votes
0answers
61 views

Is there a Closed-form distribution for a Beta-Beta distribution?

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 ...
3
votes
2answers
130 views

Probability density of sum of two beta random variables

Suppose that $X$ and $Y$ are independent and have beta distributions. $X$ has probability density function $g(x)=6x(1-x)$ for $ 0\leq x \leq 1$ and $Y$ has the probability density function $h(y)=12y^2(...
0
votes
0answers
16 views

Do betas from univariate GEE analyses equal correlation coefficients?

I have repeated data and need to determine the correlation coefficient between X and Y. Ive used GEE. Are the standardized parameter estimates from GEE (one variable X, predicting Y, repeated multiple ...
0
votes
0answers
52 views

Beta regression using GAMLSS: how to do post-hoc contrasts?

I have compliance rate data [0,1] from a mixed design study, which examines compliance rate over time for people receiving different types of incentives. I looked this up and thought that the beta ...
0
votes
0answers
53 views

What is the formula of Beta Coefficient in Logistic Regression?

I have my study about logistic regression, I have to make a software for the admission process of the school given that requirements result.. as the output to be passed or failed.. given the Logit = ...
0
votes
0answers
7 views

Change or shift the Beta distribution interval [duplicate]

I am trying to change the Beta distribution form the interval $[0,1]$ to $[0,2]$. Is that possible? I am just able to shift the distribution for example from the interval $[0,1]$ to $[3,4]$ with ...
4
votes
2answers
39 views

Why is rejection sampling with acceptance probability 2/3 for Beta(2,2) not slower than `rbeta(N,2,2)`?

I was trying to illustrate that rejection sampling is inefficient when an alternative approach is available that does not throw away samples. (This post obviously is a candidate for migration to SO, ...
3
votes
2answers
89 views

Beta as distribution of proportions (or as continous Binomial)

Beta distribution is related to binomial being also the distribution for order statistics. Probability mass function of binomial distribution is $$ f(k) = {n \choose k} p^k (1-p) ^{n-k} \tag{1} $$ ...
0
votes
0answers
39 views

Test for Equality of Parameters in Beta-Binomial Distribution

With binomially distributed data, it's straightforward to test the null hypothesis of equiprobable responses, $H_0: p=0.5$, but say you want to test the analogue in a Beta-Binomial model fit to over-...
2
votes
1answer
147 views

How to determine posterior distribution of the parameter in a binomial

Assuming that I performed n iid tests, and the total number of test is n which is a fixed value, and the observaton of 1 which corresponding to successful results is X observations yeild with ...
5
votes
1answer
90 views

Distribution of differences in beta-distribution

I want to get an analytic solution to the difference of the highest and second highest of a beta distribution. More simply, I have some datapoints on which I assume a beta-distribution. Analytically ...
0
votes
0answers
26 views

Is it valid to say higher Beta values are more significant in a regression model

I wanted to know if the above statement is always valid. For example in a simple linear or binomial regression model do variables with higher beta coefficients always have higher significant values (...
0
votes
0answers
37 views

Survival Analysis - Improbable Exp(B)?

I'm currently conducting a survival analysis on my dataset. I have data on adoption of a new service and am using a Cox Proportional Hazard Model in order to account for right-censored observations. ...
0
votes
0answers
51 views

Mixture of beta distrubutions

I have data; one column and 310 rows. When I plot the histogram, it has two peaks; see the figure. I would like to find appropriate distribution that fits the data. I tried to mixtools in R, but it ...
0
votes
1answer
30 views

Independent and dependent gives the same results?

Is there any situations where considering two random variables independently and dependently leads to same computational result ? Is there a reason why this might happen ? My specific problem deals ...
3
votes
1answer
109 views

Difference between standard beta and unstandard beta distributions?

What is the difference between standard beta and unstandard beta distributions? How to understand in an article if it is not described if it is standard or not?
1
vote
0answers
64 views

Estimating beta parameters in truncated beta-binomial distribution

I'm sampling a bunch of probabilities, $\theta_i \sim Beta(a,b)$, from a common beta distribution, and then using each $\theta_i$ to sample a value $x_i$ out of $N_i$ possibilities. However, I am only ...
1
vote
0answers
27 views

Let X_1,…,X_n be a random sample from the Beta disribution with parameters a = θ and b = 1 [closed]

I need to find the UMVUE for 1/θ but need some help. I don't know how to find a complete and sufficient statistic to start so I can't go much further. Thank you.
6
votes
3answers
147 views

Distribution of $XY$ if $X \sim$ Beta$(1,K-1)$ and $Y \sim$ chi-squared with $2K$ degrees

Suppose that $X$ has the beta distribution Beta$(1,K-1)$ and $Y$ follows a chi-squared with $2K$ degrees. In addition, we assume that $X$ and $Y$ are independent. What is the distribution of the ...
4
votes
1answer
48 views

Ancillary statistics:Beta distribution is free of $\beta$?

I am reading Robert V. Hogg Introduction to Mathematical Statistics 6th Version page 409, second paragraph. $X_1, X_2$ is a random sample from a Gamma $\text{G}(\alpha,\beta)$ distribution with ...
9
votes
0answers
109 views

Jaynes' $A_p$ distribution

In Jaynes' book "Probability Theory: The Logic of Science", he has a chapter (Ch 18) entitled "The $A_p$ distribution and rule of succession" in which he introduces the idea of $A_p$ distribution; ...
7
votes
3answers
413 views

Understanding the Beta conjugate prior in Bayesian inference about a frequency

Following is an excerpt from Bolstad's Introduction to Bayesian Statistics. For all you experts out there, this might be trivial but I don't understand how the author concludes that we don't have ...
0
votes
0answers
24 views

How Can I Combine Multinomial Data from Survey with Two Parameter Univariate Distribution

I have survey data, $X$ that measures a variable on a 1-5 Likert type-scale. I have a second variable $Z$ which, given a suitable parametric assumption, I can identify the mean and the variance but ...