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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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In fire-protection maintenance, we often need to test a sample of sprinklers that have been in service for about 25 years. Each test is pass/fail, and the parameter of interest is the failure ...
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I have the following question. I have some data $p(x)$ where each datapoint comes from averaging 100 independent binary experiments. Although it is irrelevant for the question, I am measuring quantum ...
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I'm working on a dataset of ~2900 fish, where the visually estimated sex was compared to the true sex. In about 10% of the cases (≈260 fish), the estimation was wrong (deviation = TRUE). I'd like to ...
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I have a measurement with two possible outcomes, let's say 0 and 1. If the outcome of the measurement is 1, the true value is always 1. If the outcome of the measurement is 0, there is a chance of 1% ...
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I'm using double machine learning in the structural causal modeling (SCM) framework to evaluate the effect of diet on dispersal in birds. I'm adjusting for confounding variables using the backdoor ...
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I'm not sure whether I'm assessing this problem correctly. Suppose I want do demonstrate that an adverse event occurs in less than 20% of the participants (but I hope/assume that it actually NEVER ...
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I've been looking for the best distribution to fit a glmm model to my data. The best seems to be a betabinomial model, but it gives a warning about false convergence, which is caused by large z values:...
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I was fitting the following binary glmm with glmer: ...
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I have a database of many employees, and i want to estimate how many are going to retire next year, based on many retired last year. So i thought about a logistic model like glm(retire ~ age2025 + ...
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As the question title says, I am confused why the estimated marginal means (obtained using emmeans()) for a Bayesian binomial generalized linear mixed model are so ...
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I am developing a species distribution model for a rare, data-scarce species. To explore the effect of sample prevalence, I fitted several models with different presence–absence ratios by randomly ...
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To select the correct type of data distribution (Poisson, quasi-Poisson, double Poisson regression, generalized Poisson regression, gamma, binomial distribution, negative binomial distribution, etc.), ...
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I'm working on a problem that arises in a physics context and involves probabilistic modeling using binary outcomes. I'm not a mathematician by training, so apologies in advance if I miss standard ...
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I'm interested in estimating the joint upper tail probability of two correlated binomial random variables, say: $$ X \sim \mathrm{Bin}(n, p_1), \quad Y \sim \mathrm{Bin}(n, p_2), $$ such that $corr_{...
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I want to test whether the probability of a shoot to flower depends on two factors (Modality and Group). To do this, I've used a GLMM with a binomial distribution and added a random term to account ...
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I have a model and when testing for overdispersion I used manual method and also check_overdispersion from the Performance package, and got massively different ratios (although both were overdispersed....
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It is one example in rudimentary statistics class. A professor writes a statistics test and estimates that 90% of test takers will complete the test in 1 hour or less. She gives the test to a class ...
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I have a glmm in R with 4 fixed effects, 4 interaction effects, 2 random effects, and a binomial response variable. I have two versions of this model, both with the same model strucure: ...
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I am reviewing data from a stratified random sample to describe the proportion of the total population exhibiting Trait A ($p_A$). Due to time/resource constraints, I conducted a disproportionate SRS ...
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I am writing a Python function to calculate the minimum or maximum bit-error rate (BER) in a system for a given number of transmitted bits, number of errors, and desired confidence level. I ...
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Context : I’m working with a longitudinal cohort of patients followed for substance use disorders (n ≈ 3300 observations, 900 subjects). The outcome is the number of days of substance use over the ...
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I'm running a binomial GLM to test for the effect of context (3 levels) and identity (4 levels) on the occurrence (absence/presence) of a phenomenon (specific type of vocalization). The context -> ...
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I am sorry for such a vague title, but I'll try to give a good example for my problem. Suppose, in their blood people have red and white blood cells and may (or may not) have a very small fraction (...
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I have two different processes where I want to test whether they are well approximated by a binomial distribution. My data consists of lots of triples of the form (N= number of trials, p=success ...
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Let's say we have two binomial variables $Y_1$, $Y_2$ such that for $Y_1$ number of trials $n = 103$ and number of successes $k = 51$ and for $Y_2$ number of trials $n = 53$ and number of successes $k ...
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In the Monobit Test for randomness, the threshold for passing or failing is based on a confidence interval. I understand that a 1% significance level (99% confidence) results in a larger threshold ...
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I want to give an a priori bound on the number of samples needed to obtain a confidence interval where the (a) expected width, and (b) worst-case width is $\leq \varepsilon$ using the Clopper-Pearson ...
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Let $X_1, \ldots, X_n$ be a random sample from a $\text{Binomial}(k,p)$ population where $p$ is known and $k$ is unknown. The likelihood function is $$ L(k|\mathbf{x}, p) = \prod_{i=1}^{n} \binom{k}{...
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I'm new to (generalized) linear mixed effects models. Any help would be appreciated! Below is my study design with dummy data. I'm exploring the effects of the parameters I manipulated in game 1 on ...
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I have an odd animal study design which was based on one performed in the literature, but my modifications resulted in a very complex structure... I'm using R with the ...
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This question is also posted on Mathematics Stack Exchange https://math.stackexchange.com/questions/5038432/how-do-i-make-an-m-estimator-out-of-a-glm-if-the-variance-depends-on-a-dispersio. A ...
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I am working through exercise 2.4 in Bishop's Pattern Recognition and Machine Learning. The problem asks to differentiate the normalization condition with respect to u to obtain an expression for the ...
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Suppose I have 100 fish in a pond. Each day, I decide how many fish I want to catch - a random number between 1-10 Each fish has an equal probability of being caught on any day. No new fish can enter ...
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Given a process producing a product with some constant defect rate $d$, I want to estimate the minimum sample size $n$ to confirm with a probability greater than or equal to $\alpha$ that the defect ...
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I'm trying to better understand how to select random effects in a binomial GLMM. Currently, I'm using a forward-selection approach with AIC and likelihood ratio tests, but I'm also interested in ...
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I am modeling how a a chemical reaction yield (Y) depends on the ratio between reagents (X). The higher the ratio, the higher the reagent conversion, with a clear inflection at around 1.5. Below is ...
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Question Suppose I am organizing a car auction and conducting two independent experiments: Auction A is conducted 1000 times. Auction B is conducted 1000 times. (For instance, I change the auctioneer ...
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Let's say I am flipping a fair coin. If I do m independent trials of n flips, I expect the total flips of each trial to be ...
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I have a process which succeeds with known probability $p$, and fails with probability $q = 1-p$. The process is repeated a finite, but unknown, number of times $n$. Given a number of successes $r$ (...
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I have done some reading and have re-written my question to make it a little more precise ( I hope ). It is known from previous surveys that 50% residents oppose a policy. It is decided to contact ...
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I have a dataset with 80 species which were sampled in about 120 water bodies at two time periods (historical / recent). Only presence/absence of the species in each water body is considered. The data ...
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I'm trying to calculate the probability that after, $n$ shuffles, some card ends up within the top 10 places $k$ times. I think I have got the answer, but I think I might be missing something. So with ...
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I estimated a glm with the family = quasibinomial. My dependent variable is continuous survival rate, which ranges from 0 to 1 with (like: 0, 0,1, 0,2.....,1). My ...
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Say I have N particles and I remove a fraction $f_1$ of these obtaining $k_1$ particles as $$ k_1 \sim \text{Binomial}(N,f_1) $$ and from these selected $k_1$ I have another Binomial draw of $k_2$ ...
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Chapter 13 in the book Head First Statistics deals with hypothesis testing. Its example is like the below: A drug (called snorecull) cures snore at a rate, 0.9. Then, one gets the below results. ...
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I have a model which has an accuracy of $A$. It makes a prediction with $Y$ confidence about a number of samples. Samples are observed many times, but not all are observed equally. So my data looks ...
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I am working with binned data indexed by $( i = 1, \ldots, n )$, where for each bin $i$, I have: $( X_i )$: the number of successes $( N_i )$: the total number of trials I want to model the ...
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In my province there was an election recently. In one area the conservative candidate led by 103 votes compared to the progressive candidate. Each received over 8500 votes. The other parties combined ...
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I have collected data on gender ratios that looks like this: These are counts. I evaluated 100 employees from each company, each department. And then evaluated whether they're Male or Female. ...
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I have tried reading about the concept here: https://www.ncl.ac.uk/webtemplate/ask-assets/external/maths-resources/statistics/hypothesis-testing/hypothesis-testing-with-the-binomial-distribution.html ...
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