# Questions tagged [binomial-distribution]

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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### Distribution of a single number in roullette but not chosen a priori

In roullette (say European with 37 slots) when the wheel is fair and the success is predefined as hitting a specific number (say $13$) the number of successful outcomes in $n$ spins/trials should ...
1 vote
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### Using a binomial distribution to mathematically quantify a thought experiment from my friend (python)

My friend asked me the following question: ...
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### Bivariate problem, what is the best model for this? Scoring probability depending on distance

I have been directed here from the main stackoverflow site, where i described my problem: here. Basically i have a set of sports data containing shots with their distance to the goal and the result (...
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### Given that quasibinomial regression models extra-binomial variation, why ever do binomial regression if quasibinomial is more flexible?

In reading about quasibinomial regression: The quasi-binomial distribution, while similar to the binomial distribution, has an extra parameter 𝜙 (limited to |𝜙|≤min{𝑝/𝑛,(1−𝑝)/𝑛} ) that attempts ...
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### How to aggregate survival type of data to single measure independent of time?

Thank you for the opportunity to ask this question. Since I do not speak fluently (still learning) the language of mathematics, I explain this in plain English. I understand this is too ideal but I ...
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### Binomial distribution with two probabilities

Here's the problem I have: The probability that an apple is red is 80%. The probability that a red apple is rotten is 10%. If 10 apples are picked at random, what are the odds that half are red and ...
1 vote
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### How to construct confidence intervals for multiple choice survey responses where the measurement is the percentage of respondents?

Say I have $k$ categories of responses to a survey question from $n$ respondents. Assume n of each category is about 50, so we can't just work off asymptotic behavior necessarily. How do I compute ...
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### one-sided binomial confidence interval using brute force on CDF rather than Clopper-Pearson/Wilson/etc

I was recently trying to solve a marketing problem. For say 300 trial users, only 3 converted to paying subscribers. The conversion rate for this sample is obviously 1%. And almost as obvious, we ...
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### Highly Skewed Binary Response Variable 10% One Category, 90% Other

I have a highly skewed binary response variable in my dataset. I am having issues finding a model that meets all assumptions for a binomial distribution GLM, and I believe this may be correlated to ...
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### How do we obtain the posterior of a beta binomial mixture of continuous and a discrete density?

In section 3.6 of Jim Albert's 2009 book "Bayesian Computation with R" he describes a test of whether a coin is fair using a mixture of priors. The coin tossing follows a binomial ...
1 vote
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### glm with family=bernoulli vs glm with family=binomial

What is the difference in terms of the coefficients the two yielded in R; I suppose they estimate the same thing? (Log) odds ratio? Or is the latter estimating risk/relative risk ratio?
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### Scaling variables for model selection. Unscaling for final model?

I struggle with the following question: I had to scale variables for model selection as they were in very different units and the model struggled to converge. Now that I have a final model the ...
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### Baysian Inference with beta-binomial model with different number of trials

Let's imagine that we have created and estimated a posterior with a beta prior and binomial likelihood function. The posterior is given by $p(\mu |D) = Beta(2,99)$. Now, I want to do inference with ...
1 vote
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### Combining two success runs in parallel

The goal is to calculate the reliability of a process. Here reliability is defined as follows: Definitions and tests I used Let $X$ be a random variable that is equal to $1$ when no defect is present ...
1 vote
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### Correct Distribution to Calculate Probability of Ballot Measure Success

The CA Secretary of State has historical records on ballot measures starting in 1912, and we're attempting to calculate probabilities for the 2024 ballot measures based on the historical average. Over ...
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### Proportion data with dependency using binomial generalized linear model

I did an experiment on small tree branches with closed buds were a box containing 30 branches was monitored 3 times per week for the presence of leaves. The number of branches that have reached a ...
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### multiple comparison with a binomial model in R

When performing a multiple comparison in a binomial model, I encounter a problem when one of the groups has the probability of success = 1. For example, ...
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### $N \sim$ Poisson iff number of heads & tails independent?

Consider $N$ to be the total number of fair coin tosses such that $N \sim \mathrm{Pois}(\lambda)$. Then for the events (sorry) random variables defined as, $A:$ No. of heads observed and $B:$ No. of ...
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### How can I plot interactions of standardised coefficients from a binomial logistic regression?

I'm using the mvabund package to run a model of species presences as a function of a trait matirx and an environmental matrix. The '4th corner' terms are the ...
1 vote
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### Coding error? Why is the treatment not showing as a significant effect with GLM and standard error is so high?

I've been handed off some data to analyze and I'm looking for something simple and straightforward. The main study question is testing the efficacy of 7 herbicides, with one untreated control. The 1 ...
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### Calculating probability curve of a binomial sample

Apologies, I'm not a stats-person, I'm looking for a concept that I'm struggling to Google. I have a boolean function that returns true or false at some unknown chance c. I have a sample of 100 ...
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### How to generate binomial point estimate consistent with a binomial confidence interval?

Consider this sample data: ...
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### Binomial vs product of binomial in likelihood for Bayesian inference

I am working through McElreath's book on statistical rethinking. One of the problems is the following: Using grid approximation, compute the posterior distribution for the probability of a birth being ...
Consider the random variables $a_i,i=0,1,\ldots,n$ be random variables which take values from $\{-1,1\}$ independently and randomly with equal probability. Let \begin{align} S &= a_1+\cdots+a_n , ...