The binomial distribution gives the frequencies of "successes" in a fixed number of independent "trials". Use this tag for questions about data that might be binomially distributed or for questions about the theory of this distribution.

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Help for Binomial Distribution question

I am having issues with understanding a question on an assignment: A test for the presence of a certain disease has probability 0.05 of giving a false-positive reading and probability 0.04 of ...
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Upper bound for asymmetry using skewness

Can the following quantity be upper bounded by the (standardized third moment) Skewness of $X$ ($\mu_3/\sigma^3$)? $$\left|\mathbb{P}(X \geq \mathbb{E}X) - \mathbb{P}(X \leq \mathbb{E}X)\right|$$ I ...
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Counterexample against binomial assumptions

The question is from a Master-level Probability Course. It is well known that the underlying assumption for the binomial distribution is that there are n independent Bernoulli trials. More ...
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Dealing with an uncertain number of trials

I've got a binomial distribution where I'm trying to figure out the probability of success (specifically, the odds of a certain event in a video game). This would be simple enough, except that I ...
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Probability of a sum of values from a number of dice rolls

4 six-sided dice are rolled independently. Compute the normal approximation with continuity correction for the probability of rolling a total of at most 6. I have arrived at a point where I got that ...
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1answer
28 views

Find MLE by combining two different experiments

I am trying to solve the following problem on an assignment. Anna has two dice. Die $F$ is fair: it rolls $1,2,3,4,5$ or $6$ with equal probability $\frac{1}{6}$. Die $D$ is dodgy: Anna suspects ...
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Hypothesis testing with multiple variables

I'm trying to understand the process behind testing both A/B site changes for statistically significant increases in conversion rate, and also how then to expand this to testing multiple variables. ...
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binomial test for over-represented kmers in biological sequences - what is the right test?

Imagine you have a long string, like a genome, and you split it up into every overlapping word of size n. This is called a kmer. ...
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Estimation probability in related binomial distribution

I have two binomial experiments with an unknown probability - But i do know that the ratio between the probability in the first experiment and the probability in the second experiment - For example I ...
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53 views

Standard error of proportions, with weighting

I have a set of experiments $i=1\dots k$ each of which performs $n_i$ binomial experiments, recording a fraction $p_i$ successes. Clearly if I trust all of the experiments equally, my estimated ...
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27 views

Using the binomial distribution to identify chance-level responses

I have a subject who was giving 2-alternative forced choice responses for a task consisting of 80 trials. For each trial, there was a 50% chance for each of the two options to be correct. This means ...
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Problem solving a simple probability exercise

I'm currently studying a Statistics course and I'm trying to solve a simple probability exercise: A production facility employs: 20 workers on the day shift 15 workers on the swing shift 10 workers ...
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159 views

Why does SAS PROC GLIMMIX give me VERY different random slopes than glmer (lme4) for a binomial glmm

I am a user more familiar with R, and have been trying to estimate random slopes (selection coefficients) for about 35 individuals over 5 years for four habitat variables. The response variable is ...
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1answer
36 views

How to sample from “biased” binomial distribution (ideally in python/numpy)

I need to sample a variable from a distribution that's like a binomial distribution except with a "bias", I'm not sure what it may be called: $p(X=k)$ is proportional to $k.B(n,p)(k)$ where $B(n,p)$ ...
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1answer
64 views

How to model a count dependent variable with upper limitation

I have a dependent variable, which have 0, 1, 2, or 3 for its value. I asked participants to choose three items and coded 1 if it is in a certain category and 0 otherwise. I add the three binary ...
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2answers
216 views

Bayesian estimation of $N$ of a binomial distribution

This question is a technical follow-up of this question. I have trouble understanding and replicating the model presented in Raftery (1988): Inference for the binomial $N$ parameter: a hierarchical ...
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Estimating $n$ and $p$ for Binomial distribution, repeated counting of partly hidden population

A brief motivation: $n$ critters live in an aquarium, where sadly they often hide in, under or behind things. When the aquarium is observed, each critter is only seen with probability $p$ ...
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2answers
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Test if two binomial distributions are statistically different from each other

I have three groups of data, each with a binomial distribution (i.e. each group has elements that are either success or failure). I do not have a predicted probability of success, but instead can ...
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Identifiability in generalized linear random effect model?

Suppose I observe binary $Y_{ij}$ for $i = 1, ..., N$ and $j = 1, ..., J$ and I want to model $$\Pr(Y_{ij} = 1 \mid \lambda_{i}) = \Phi(\lambda_{ij}), \qquad [Y_{ij} \perp Y_{ij'} \mid \lambda_i]$$ ...
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Posterior distribution of proportional difference of two binomial variables

Can somebody point me in the right direction for a treatment of the following problem? I imagine this should be a fairly common problem in medical statistics... Given two binomial random variables ...
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1answer
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Formula for calculating sample size for hypergeometric distribution

Suppose you have an urn with "N" marbles. All marbles are either black or white. You take a sample of size "n" without replacing them to the urn. With this one sample you would like to be able to ...
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1answer
30 views

Binomial data and PCA and cluster analysis

I have obtained responses on around 48 items measuring employer attractiveness. The goal of my analysis is to cluster respondents according to these employer attractiveness dimensions. I plan to ...
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62 views

Analytic or sample standard deviation with binomial data

I've been looking for recommendations on whether it's better to use the sample standard deviation (SD) for a binomial distribution or use the analytic SD (or variance). It's for experiments with ...
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Correcting for multiple testing on non-independent sliding windows

Question Values taken from adjecent windows in a sliding windows are corrolated. If I calculate a p-value from each window, how can I correct for the fact I have tested many windows, given that the ...
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1answer
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Comparing polynomials

I've got a bunch of data on pop singers' performance on the Hot 100 charts over time, and I'm trying to compare the early part of different artists' careers. For example, I might look compare Miley ...
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Binomial random variable conditional on another one

On the Wikipedia page for the Binomial distribution, the following property is mentioned (under the related distribution section): (paraphrased) If $X\sim \text{Bin}(n,p)$ and $Y|X \sim ...
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How can I do a test for proportions when the data has been collected weekly from the same general population?

So I have a series of proportions taken weekly for 7 weeks. This is a study of which way spiders were facing. So for example, the first week, 20 spiders were facing out, and 10 were facing in. Now I ...
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Conditional on binomial question

Here goes the question from textbook: A small restaurant seats 20 diners, and is full every night. The chef knows from previous experience that 40% of the diners order steaks, so she always has 12 in ...
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Bootstrap of parameter estimates and confidence intervals (hurdle model)

Think you can help with this. I´ve run a set of candidate hurdle models on insect abundance data with pscl package for R. These models had an abundance part with a truncated negative binomial ...
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1answer
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Using a binomial approach to calculate significance of multiple significance tests

I have 10 data sets with normal distributions and carrying out significance tests on each one. With this many data sets, there is a good chance that some will be significant by chance. I am going to ...
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Difference test for beta–binomial variables

Let $X \sim \textrm{Beta–Binomial}(\alpha_1, \beta_1, n)$ and $Y \sim \textrm{Beta–Binomial}(\alpha_2, \beta_2, n)$ and write $\mu_1 = \frac{\alpha_1}{\alpha_1 + \beta_1}$, $\phi_1 = \alpha_1 ...
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Sample probability for binomial distribution

$X\sim B(40, 0.3), \bar X$ is the sample mean, and $n$ is number of observations. I need help in finding $P(\bar X\ge13)$ for a sample of $49$. I have tried the following, please guide. $\mu=40 ...
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EM for Mixtures of Bernoulli (M-step)

When applying the M-step for a mixture of Bernoulli distributions, one of the parameters in our maximization is the Bernoulli parameter $\mu_{k}$, where $k$ is the index of the "mixture component", ...
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Probability of $k$ successes in no more than $n$ Bernoulli trials

I feel like these questions should be related to the binomial and geometric distributions, but I can't quite work out how. Suppose I do sequential independent Bernoulli trials each with success ...
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Cooccurence of Two Categorical Variables

I am trying to calculate if there is a dependence between two categorical columns, or a significant cooccurence of two categorical variables. Let's say I have columns A and B, and and out of 200K ...
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How to specify binomial glmm with random and correlation in R?

I am working on developing a model with a binomial response variable. My data consist of GPS points from tracked animals. The data set is large and contains 15,000 observations from 40 individuals. I ...
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Binomial model of true/false test taker

I have a very large number of true/false questions. I want to take a sample of these questions and use them to test a subject. I would like to infer the proportion of questions out of the larger set ...
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GLM with categorical predictor on R

I need to do a model with a generalized linear model. My data are these: habitat : 0 or 1, group : 1 or 0 , mortality : yes or no, and the numbers of individuals for each case (habitat, group and ...
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Trying to figure out a formula and answer to probability question

If I go to a certain establishment 12 times in one year (let's just say once a month), and there's a 6.25% chance each time that I go in there that I would run into a person I know, what is the ...
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Best proportions test based on counts (accuracy, distribution, etc)

I'm trying to compare two sets of counts over totals. For example, subject 1A will have 40 out of 600, and subject 1B will have 3 out of 20. How do I compare these proportions and counts while taking ...
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How to fit a longitudinal model with binary outcomes

I'd like to fit a longitudinal model for where multiple subjects experience binary outcomes over time. To accomplish that, I'd like to use an additive random effect for each subject and an ...
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Power analysis for binomial data when sample sizes are different

I'm running an A/B test where I want to compare two different layout of a button and want to see if one layout lead to a higher Click-Through Rate with a certain statistical power. I want to use a ...
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2answers
169 views

How many answers to memorize for a test?

Recently one of my friends asked me this deceivingly simple question: I have a midterm with a predetermined list of 15 possible questions. Out of the 15 questions only 7 will actually appear on ...
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sum and product rules of probability

I am reading Bishop's Pattern Recognition and Machine Learning. In page 73, chapter 2.1. I can't understand the formula 2.19 : $$p(x=1|\mathcal{D})=\int_0^1 p(x=1|\mu)p(\mu|\mathcal{D})\text{d}\mu ...
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1answer
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Caculate Type II error for Binomial distribution

Basically this is a question if I got the general idea behind the Type II Error right. I’ll set up a little reproducible example: Given $p_0=0.6$ with an $\alpha$-level of $\alpha=0.1$. As Binomial ...
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1answer
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Confidence interval for N, based on binomial

I've searched the web and these forums but couldn't find a subject that resembled my problem. If I missed something then I'd like to apologize upfront. My problem is this. I have a given probability ...
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What is a cumulative Binomial probability?

I am new to this so don't know if I am asking the right question as I just read about its usage but didn't know what exactly a cumulative Binomial probability is. So my question is: What are ...
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Test for aggregation of binary events/successes (binomial/glm??)

this has been vexing me for a while and I can't seem to solidify an answer beyond vague thoughts about Poisson distributions. I think this is a simple problem and I'm missing something obvious. Any ...
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How to apply the random statement in my model?

i am trying to model the following data in SAS using proc glimmix and i would like feedback if i have modelled my data correctly. My data consist of individual chickens (ID) who are grouped by ...