Questions tagged [beta-distribution]
A two-parameter family of univariate distributions defined on the interval $[0,1]$.
0
votes
0answers
20 views
Uniform conjugate prior for a Beta distribution
Given
$$
\pi \sim \text{Beta}(\alpha, \beta)
$$
I'd like to place a prior on $\alpha$ and $\beta$. The "trick" mentioned in this post and this post seems to be to recognize that since
$$
\begin{...
-1
votes
0answers
16 views
Likert Scale data analysis [closed]
I have a dataset where judges give singers scores on Likert Scale on various attributes. Now we are to find what their ranks should be. Now usually normal distribution is assumed, but my teacher asked ...
0
votes
0answers
14 views
Evaluating model fit for glmmTMB with beta distribution
I am looking for a way to evaluate model fit (e.g. R2, %deviance explained) for the following model:
m1<-glmmTMB(AUC_indep~woody+dispersal+log_densitys+log_seedwts+I(log_seedwts^2)+(1|modeltype), ...
4
votes
3answers
161 views
Proving transformations of two independent chi-squared random variables is equivalent to a Beta distribution
I came across the following in some old class notes of mine:
if $\chi_{v_{1}}^{2}$ is independent of $\chi_{v_{2}}^{2}$ then
$\frac{\chi_{v_{1}}^{2}}{\chi_{v_{1}}^{2}+\chi_{v_{2}}^{2}}\backsim
...
2
votes
1answer
48 views
Moment Generating Function of Beta ( Taylor series)
Suppose X is a random variable with a Beta ( a =$\frac{1}{2}$ , b=1) distribution and
x in (0,1)
Then the moment generating function is calculated as below
$ M_X(t) $ = $\mathbb{E}[e^{tX}]$ =$ \...
0
votes
0answers
34 views
Logistic regression - binary to continuous - how to interpret?
Given data with a binary outcome, i.e.: $0$ = no event, $1$ = event
which can be modeled with logistic regression, how then do we understand the following logic:
...
0
votes
0answers
46 views
R package for meta-analysis of beta-distributed data
I am conducting a meta-analysis, and my effect sizes are proportions, with a credible interval for weighing. I think I should assume a beta-distribution, but I do not know which package to use. This ...
1
vote
0answers
26 views
Expectation of Sufficient Statistic for Beta Distribution
I am looking at question 1b of the following notes: http://www.gatsby.ucl.ac.uk/teaching/courses/ml1/asst1.pdf
In 1a, I have shown that the Beta distribution has a density that can be written in the ...
0
votes
0answers
12 views
0
votes
0answers
22 views
Uber's Pyro less accurate than expected on toy example
Trying to understand the pyro example here:
https://pyro.ai/examples/svi_part_i.html
which starts with a Beta(10,10) prior, adds 10 Bernoulli likelihood datapoints with a 6,4 split. The analytic ...
1
vote
0answers
47 views
MLE for Beta distribution, with $\beta$ = 3
I'm trying to calculate the Maximum-Likelihood Estimator for $\alpha$, using the beta distribution with $\beta = 3$. I'm kind of stuck at the last bit. Perhaps I've made a mistake somewhere, or this ...
1
vote
1answer
71 views
If $X\sim\text{Beta}(\theta,1)$, obtain the confidence interval of $100(1-\alpha)\%$ based on the asymptotic distribution of the score function
Let $X_{1},X_{2},\ldots,X_{n}$ be a random sample whose distribution is given by $\text{Beta}(\theta,1)$. Obtain the approximate confidence interval of $100(1-\alpha)\%$ based on the asymptotic ...
0
votes
0answers
17 views
Is fair to compare Dirichlet to a Multivariate Beta regression?
I am conducting some analysis on my data I found a strange behavior and would greatly appreciate some guidance or suggestions.
I am trying to investigate the effect of a categorical variable (cl) to ...
1
vote
1answer
26 views
Valid highly informative prior for proportion
I am trying to find a prior distribution for a proportion $\theta$ that is highly informative i.e. it is almost point mass at $\theta$ but I am not able to find such distribution that is valid for a ...
1
vote
0answers
30 views
Squared internally studentized residual over $n-p$ is Beta distributed
Assume a regression model $y = X \beta + \varepsilon$ with $n$ observations and $p$ parameters. Let $r_i$ be the $i$-th internally studentized residual:
$$r_i = \frac{e_i}{\sqrt{\hat{\sigma} (1 -h_{ii}...
0
votes
0answers
18 views
Model reputation with beta distribution
I am trying to develop a reputation score in which the reputation is calculated by the ratings that buyers give to sellers. What i am trying is to replicate a paper very well known http://faculty.neu....
2
votes
1answer
36 views
Efficiently Computing The Beta CDF [duplicate]
I am using numba to JIT compile some looped python functions as part of a larger application. Ideally, everything will run in numba's "no python" mode, such that the loop can be parallelised.
One of ...
1
vote
1answer
49 views
Understanding the Bayesian question [closed]
I have a Bayesian question here:
In a drug experiment, patients with a chronic condition are asked to choose between two drugs, C (control), and T (new treatment). (You may assume for the purpose ...
0
votes
0answers
39 views
What is support of beta distribution? [duplicate]
I do know that the probability density function of beta distribution is
$$
\frac{x^{\alpha-1}(1-x)^{\beta-1}} {\displaystyle \mathrm {B}(\alpha,\beta)}\!
$$
where
$$
{\displaystyle \mathrm {B} (\...
1
vote
0answers
51 views
Can't understand the Beta distribution as described in this paper
I'm reading through the following paper (1). On page 2, section 2.1, there's a description of the selection of a beta distribution used:
Since both the choice of s and the strategy for handling the
...
1
vote
0answers
58 views
Distribution of dot products of two random independent unit vectors in $D$ dimensions
Duplicate of the stats stack exchange question here; however, I need some help with some of the steps in the accepted answer.
A uniform distribution on the unit sphere $\mathbb{S}^{D-1}$ is
...
0
votes
1answer
27 views
Proportion/Rate data and zero-inflation (two counts)
I have an experimental dataset which makes use of two counts. Using vague terms, we are studying animals as they become behaviourally inactive and then apply a stimulus once an hour. One of the counts ...
1
vote
0answers
14 views
How to relate beta CDF to student-t CDF? [duplicate]
We can relate the student-t and beta distributions as such:
If $X$ has a Student's t-distribution with degree of freedom $\nu$ then one can obtain a Beta distribution:
$$\frac{\nu}{\nu + X^2} \...
2
votes
2answers
33 views
Interpretation very small standardized coefficient beta
In one of my studies I have results similar to the below:
β=-0.0007 (95% CI: -0.0009, -0.0002), p=0.01
Since β is so small (but also the Confidence Interval (CI)), is this result still meaningful?
...
0
votes
0answers
19 views
In a manuscript, is an incomplete beta function a useful simplification of a sum, if the argument ends up negative?
I'm working on a manuscript which I intend to submit to a statistics journal. I have a sum which I "simplify" to the regularized incomplete beta function $I_{-t}(a,b)$, where $t$ is a positive real ...
0
votes
0answers
9 views
Can I improve an estimate of a coin-flip probability from a single trial using an imperfect oracle?
I have the following generative model:
I have a unknown random variable $S\in[0,1]$ and samples $s_i \sim S$. I do not observe $s_i$ directly, but instead an imperfect oracle $q_i$, which might or ...
0
votes
0answers
13 views
Appropriate statistical test for continuos bounded r.v
I have a number of continuous random variables bounded in the domain [0,b] and I need to perform a statistical test to check whether their average is different from ...
4
votes
0answers
34 views
Beta-binomial distribution for scaled and translated Beta
Recall, that a binomial distribution in which the probability of success at each trial is randomly drawn from a beta distribution results in the so called beta-binomial distribution. One can calculate ...
3
votes
1answer
50 views
Why p-values are not significant even though AIC values improved a lot in model selection using GAM mix modelling and beta regression
Dear StatExchange community,
I am studying disease progression in plant leaves and I am trying to estimate differences between a wild-type and a mutant plant. To achieve this I am using the ...
2
votes
0answers
51 views
In a bivariate normal sample, why is the squared sample correlation Beta distributed?
If $(X_i,Y_i), i = 1, \dots, n$ are independently bivariate normal distributed, with mean $(\mu_x , \mu_y)$ and variances $(\sigma_x^2, \sigma^2_y)$ and correlation coefficient $\rho = 0$.
Denote $T =...
0
votes
1answer
87 views
Simulate from a mixture of two beta distribution [closed]
I have this distribution :
$X \sim 0.75\mathcal{B}e(\alpha_{X_1}=1,\beta_{X_1}=3)+0.25\mathcal{B}e(\alpha_{X_2}=5,\beta_{X_2}=1.75)$
where the density function is given from this function:
...
1
vote
1answer
75 views
Mean of a truncated non-standard beta distribution
I have a non-standard beta distribution in the interval [-0.02 , 0.005] (as opposed to [0,1]).
I know its mean and variance (and thus α and β).
I want to calculate the mean of its truncation to [0 , ...
0
votes
2answers
28 views
All positive Beta exponents in a binomial logistic regression
I'm running a regression in which the predictor is a categorical measure of living arrangement (1=two parent household, 2 = single parent, etc). There are 8 total categories in this variable. I'm ...
1
vote
0answers
30 views
Question regarding FamaMcBeth regression
I'm new here and hope you can help me with three questions I'm having in regard to the FamaMcBeth regression methodology.
What is the advantage of using firm specific returns instead of an aggregate ...
0
votes
0answers
69 views
Change point detection in beta distribution
If the outcomes of agent is modeled as a Bernoulli distribution with success probability θ ∈ [0, 1]. Where α is number of successful tasks that agent execute, and β is number of unsuccessful tasks ...
0
votes
0answers
24 views
Power Analysis with Noncentral F distribution
I'm looking to replicate a power analysis for binary data using an MRMC analysis (details found here). The data looks like this, where Score is a binary variable.
...
1
vote
1answer
44 views
Probability that one random variable using the Beta Distribution being greater than another, bounded intervals
I am doing some practice problems to prepare for my statistics exam, and I just want to know if my reasoning is correct on one problem, and if not, I want to know how I should reason through this. The ...
0
votes
2answers
94 views
Independence of Beta ratios of Gamma variates
If $X= x_1/(x_1+x_2+x_3)$ and $Y= x_2/(x_1+x_2+x_3)$ where $x_1, x_2, x_3$ are independent $\chi^2$-distributed random variables with d.f. $-n_1,n_2, n_3$ respectively. Are $X$ and $Y$ independent?
I ...
0
votes
1answer
48 views
How to justify using Beta distribution as a prior distribution in the following problem
Let $\theta$ be the proportion of people who are ready to quit smoking within 6 months. Let's say we perform a survey in $2017$ with a $n$ volunteers who ask people this question until they obtain yes ...
0
votes
2answers
30 views
Beta distribution and normalization [duplicate]
Here in the 4 pictures in the last answer, is the vertical axe
the probability? I.e. it seems to me that it is somewhat unnormalized : it has the value 2 in the 2nd picture and 3 in the 3rd picture. ...
0
votes
0answers
40 views
Self Study - How does $\alpha$ and $\beta$ correspond to mean and variance of a beta distribution? [duplicate]
I am trying to figure out how to provide $\alpha$ and $\beta$ in terms of $\mu$ and $\sigma$ in a beta distribution.
$\mu$ is given as $\mu = \frac{\alpha}{\alpha + \beta} $
$\sigma$ is given as $\...
0
votes
1answer
12 views
Analysis in a beta simulation
I did a simulation where shape1=1 and shape2=2, for n=10, n=100 and n=1000, the following is:
...
1
vote
1answer
59 views
How to model a binary vector by the Beta-Bernoulli distribution in R or Python？
I have a set of data $x=(x_1,x_2,x_3,...)$;e.g:$x=(0.1,0.003,0.78,...)$
which follows a beta distribution. Since $x_i$ in my data $x :x_i ~ Bernoulli(p)$, where $p$ is the prior of average $x$ and ...
0
votes
0answers
26 views
Simulate a 2D-beta distribution: spatial simulations
I'm doing spatial simulations and I would like to simulate a matrix that represent a truncated 2D-bimodal distribution with U shape. In other words, I would expect high density towards the borders of ...
1
vote
1answer
330 views
How to pick starting parameters for MASS:fitdist() with the beta distribution?
I have data set of ~700k yes/no events that I want to first aggregate on various features (e.g. group by average), always resulting in a 34 length vector. From there, I want to fit a beta ...
8
votes
1answer
148 views
Finding the distribution of sample range for a Beta population
Let $X_1,X_2,\ldots,X_n$ be i.i.d random variables having density
$$f(x)=2(1-x)\mathbf1_{0<x<1}$$
I am trying to derive the distribution of the sample range $R=X_{(n)}-X_{(1)}$.
The ...
4
votes
0answers
69 views
How to infer a prior belief after observing a behavior
My participant goes through a maze made of 32 T intersections. At each intersection he must choose whether to go either to the left or to the right: one option will lead to another T intersection, ...
0
votes
2answers
58 views
How to convert the parameters in a binomial distribution to those in a beta distribution?
I know that the beta distribution is the generalized continuous case of the discrete binomial distribution. Let's say I have a binomial distribution, $B(N,p)$. I would like to know the corresponding $\...
0
votes
0answers
57 views
calculating credible intervals for Bernoulli trials with a beta-distribution
I'm interested in finding credible intervals for Bernoulli trials with a variable probability of success.
So, the process (as I understand it) is the probability of success, p, is modeled with a ...
0
votes
1answer
36 views
how can this missing observation model be extended to include cases where sigma is a function of other variables?
Richard McElreath's blog entry Algebra and the Missing Oxen describes a simple missing observation model in RStan. At the end of the blog, he says it can be extended easily to cases in which the ...
