Questions tagged [bernoulli-distribution]

The Bernoulli distribution is a discrete distribution parametrized by a single "success" probability. It is a special case of the binomial distribution.

338 questions
12 views

21 views

Bernoulli equivalent to the covariance matrix

I'm looking for a parametric model for the density of binary variables. Say, a few hundred. For continous variables I there is the Gaussian model. I can estimate mean and covariance matrix from data. ...
13 views

Binary models with the regressor that has Bernouli distribution [closed]

I have a binary dependent variable, but my regrerssor also has Bernouli distribution. Will logit still give a consistent estimator in this case? How can I estimate? Is that right? model: y=b1+b2*x b1=...
36 views

Bernouilli variables - bias and variance of estimator

Reading through this I work on Example 1 in 3. Consistency. $X_{1},... , X_{n} ∼ Bernoulli(p)$. The mle $\hat{p}$ has bias 0 and variance $p(1−p)/n \rightarrow 0$. Here $\hat{p} = \sum_{i} Xi/n$. ...
33 views

Hypothesis testing on a Bernouilli variable

I have a Bernouilli variable which is $1$ with probability $p$. I need to test the hypothesis $H_0:p<\theta$ vs. $H_1:p>\theta$, where $\theta$ is a given constant. The question is to find $n$ ...
76 views

17 views

How do we perform residual analysis on binomial model with small counts?

I know that both Pearson and Deviance residuals tend to be approximately normal for Poisson and Binomial model with large counts when standardized, so we can exploit that to perform the residual ...
125 views

Evaluating goodness of fit for Bernoulli glm [duplicate]

I am trying to fit a model estimating the success probability of the Bernoulli distributed random variable with the logistic link function. However, I am stuck with testing the goodness of fit of my ...
53 views

Two approaches for finding a MLE in a binomial setting

I'm learning towards an exam in mathematical statistics and I came across the following question. I was wondering if the second approach of solving the question is legitimate. If both are correct, is ...
100 views

Bernoulli distributed random variables - Change point Detection

I am looking for change point detector model for my Bernoulli random variable. I built my simple detector, the absolute difference between stander deviation of of all transaction history stored, and ...
42 views

Specifying frequency parameter in the absence of occurrences

Let's say I have a process where the occurrences are independent, proportional to time. I made $n$ observations for which I only observed no occurrences. My goal is to define a frequency parameter and ...
32 views

I want to simulate a random sample of length n from DAG of correlated Bernoulli's

Suppose I have a DAG of 4 vertices. Each vertex consists of a Bernoulli of parameter $p$. It is the following: (Z) ---> (Y) (Z) ---> (W) (X) ---> (Y) ---> (W) I hope it is clear. Anyway, I ...
167 views

CDF and MGF of a Sum of a discrete and continuous random variable

I am currently dealing with the following exercise: Given the random variables $X \sim Be(p), Y \sim Exp(\lambda)$, and assume they are independent. Set $Z:= X + Y$. Compute the Moment Generating ...
24 views

Bernoulli distribution/ SOME probability/conjugate prior

I would like to know what "SOME probability of seeing tail" means in the second answer here. I.e. how much is it? EDIT: I do not understand how can I see that there is SOME probability of seeing Tail ...
183 views

The distribution of the product of a Bernoulli & an exponential random variable

Let $X$ be an exponential random variable $f(x) = c e^{-c x} \text{ if }x > 0; 0 \text{ otherwise.}$ Let $Z$ be a Bernoulli RV with $Pr(Z=1)=0.45$ and $Pr(Z=0)=0.55$. $X$ and $Z$ are independent. ...
107 views

88 views

Finding MLE of $p$ where $X_1\sim\text{Bernoulli}(p)$ and $X_2\sim\text{Bernoulli}(3p)$

Let $X_1\sim\text{Bernoulli}(p)$ and $X_2\sim\text{Bernoulli}(3p)$ be independent Bernoulli random variables where $p\in[0,1/3]$. Derive the MLE of $p$. We have that L(p\mid \vec{x})=p^{x_1}(1-...
14 views

Does mixture of sigmoids make sense given the theories about mixture of bernoullis?

Mixture of bernoullis is the combination of bernoulli distributions, which can be illustrated by the sampling process of K bags of D coins, here is a quick tutorial about it https://cedar.buffalo.edu/~...
208 views

...
372 views

Maximum likelihood estimator for Bernoulli parameter based on standard normal

$X_i \sim Normal(\psi,1), \ \ i = 1, ..., n$ $Y_i = 1$ if $X_i \ge 0.$ $Y_i = 0$ if $X_i < 0.$ Let $\theta = P(Y_i = 1)$. What is the MLE of $\theta$? I know how to find the MLE of a Bernoulli ...