Questions tagged [binomial]

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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11 views

Augmented binomial test where p is different for each trial

A have a model process whereby for each item, $i$, of $N$ total items I estimate a trial success probability $p_i$. I then have results for each individual process which has resulted in failure (0) or ...
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Can proportional binomial regression be used in piecewise structural equation modelling (piecewiseSEM)?

I'm using generalized linear mixed models from the lme4 package to do structural equation modelling using piecewiseSEM. It works ...
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Confidence interval for average of different binomial trials - can I apply central limit theorem?

I have person-level data, and for each person, I have the racial breakdown of the geographic area in which they live. For example, person A might have 100 people in their area, and 80 (80%) of them ...
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Selecting between a zero-inflated binomial, OLRE and beta-binomial model

I need some help in deciding which of the following models fits best the data that I have. This was a survey where participants reported proportions of successes (defined as n/m) in condition A and B. ...
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How to calculate a confidence interval in R for a binomial mixed-effect model (which was fit using the R package glmmLasso)?

How does one calculate confidence intervals for a binomial mixed-effect model that was fit using the R package glmmLasso? I am interested in the 95% confidence intervals for the fixed effects. confint ...
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Determining a safe number of parking spaces

A company is building 100 new apartments. Based on previous data from similar areas, the company knows that the propability is 25% that a household will not have a car, 50% that a household will have ...
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54 views

Binomial distribution index

I stumbled against this problem and found it really hard and help would be much appreciated Let $X_{1},X_{2},......,X_{n}$ be a series of independent Bernoulli variables with $P(X_{i}=1)=\theta$ and $...
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Difference between Variance $\sigma^2$ and variance in binomial distribution

I am reviewing some basic statistic concepts. Now I am not sure what 's the difference between variance $$\sigma^2=\frac{1}{N}\sum^N_{i=1}(x_i-\mu)^2.$$ and binomial distribution $$\mathrm {Var}(X)=np(...
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Measures of variance for binomial distribution - “maximum” and “chance” values

I've come across a rather old textbook on statistics (Statistical Methods in Medical Research, P.Armitage, 1977) and in the section on binomial distribution there is an example that uses terminology I ...
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38 views

Binomial theorem vs probability of a sequence

In Daniel Kahneman's book "Thinking, Fast and Slow", he offers the following example of how our minds identify causal patterns out of random chance. A hospital has 6 babies born in a day. We ...
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Distribution of population size $n$ given binomial sampled quantity $k$ and selection probability $\pi$

Given a drawn (without replacement) sample size $k$ from a binomial distribution with known probability parameter $\pi$, is there a function which gives distribution of likely population size $n$ from ...
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GLM with binomial function in R with Tukey HSD comparison

I need help to calculate the binomial function using glm model in R for the below data can anyone help me to find how to arrange data commentary and analysis codes.
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Confidence intervals for the probabilities of each outcome in a multinomial [duplicate]

I have a survey that includes questions where you can choose one option from a list. For example: "How often do you go to the supermarket?" ...
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Gamblers Ruin with multiple coins tossed at the same time

I'm quite ashamed to be stuck with a Gambler's Ruin problem, I guess I'm missing some basic statistical intuition here: Three fair coins tossed. Heads gets +1, tails -1, pay-offs are added and net pay-...
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Sample size relative to true error

Say I have a distribution X, which is made up of n real numbers I have a subset K of X I also have two more subsets Y and Z, which each contain j samples from X How large does j have to be for the ...
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How do I analyze bimodal distibuted data with a linear mixed model

The experiment I am working on has the following design: A B C D E F B A D E F C A B E F C D B A F C D E Each Letter represents a different level of the single factor called “...
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Strange behaviour for binomial GLM in R when changing family

I am undertaking some data analysis in R where I fit a binomial GLM to some data using the glm function. The model is called ...
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217 views

Why is CDF of binomial random variable step function

I just read that the cumulative distribution function for a binomial random variable is a "step function where the function is flat and then jumps at each nonnegative integer value". Can ...
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How to estimate the minimum required sample size to reach a certain significance level for a binomial test?

I'm about to conduct an experiment where I will measure a binary variable. I will test two different settings of a machine and then I want check whether these two settings yield different proportions ...
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50 views

Sample size for binomial distribution for rare events

I would like to estimate the parameter p in a binomial process but need to determine the sample size required. I believe the event is fairly rare, and I have read the normal approximation may not be ...
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Response variable with values 0 and 1: logistic regression vs bernoulli vs binomial

I have a response variable X with values 0 and 1. I can use it as an integer or as a factor in regression. I use brms package for modelling. The families of brms are: https://rdrr.io/cran/brms/man/...
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Why do epidemiologists fit the number of transmission cases with negative binomial distribution?

In the recent paper on coronavirus spread in Hong Kong, the number of individuals infected by one person (relative to all transmission cases) is fit by a negative binomial distribution. Why is that? ...
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Reformulation - Probability of correctly inferring whether a coin can produce heads

[This is a repost, since the original post specified a slightly different problem than I actually had in mind] Suppose you have a coin which you know could be biased towards tails with unknown ...
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Conditional expectation when more than certain number of heads are observed out of 'n' trials

Suppose a coin is tossed $n$ times and it is then observed that the numbers of head (the success event) appeared is at least $k<n$. I'm interested in knowing the conditional expectation of no. of ...
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Estimation of CDF in multiple points

Suppose we have a sample $X_1, \ldots, X_n$ of i.i.d. real-valued random variables with an (unknown cumulative) distribution $F$. The goal is to estimate the value of $F$ in multiple points. That is, ...
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Calculating confidence intervals for each class in a frequency distribution for a binomial distribution

This is a question from the book "Statistical Methods (6e) by Snedecor, Cochran": 10 balls, numbered 0 to 9, are placed in a box. For our sample, a ball is drawn from the box and then ...
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Why is the permutations of 6 objects where 2 are similar and the other 4 are similar is the same as 6c2?

I'm studying binomial expansion, and to get all the outcomes or arrangements of head appearing twice after throwing a coin 6 times without using a tree diagram, it's written that we can use 6c2 to get ...
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Finding posterior probability mass function of binomial parameter

Question: Suppose a lot containing 1000 items is received from a supplier containing parameter (unknown) defective items. The past experiences with this supplier suggest that 5% of items in a lot are ...
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Expected value of unbiased estimator of $\sigma$ in binomial sum

Suppose that $Y_1, Y_2, \dots, Y_r$ are random independent variable such as $Y_i \sim B(m_i, \pi)$, the idea first is to find $\hat{\pi}$ which is the maximum likelihood estimator an use it to find ...
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Confidence interval for a binomial proportion when the number of trials is uncertain?

Hopefully a simple question; here's the setup: I'm trying to estimate the prevalence of a medical condition in a specific population. The size of the population(s) of interest is itself uncertain. I ...
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Probability hotel reservations

A hotel has 100 rooms, and charge guests for their rooms in advance. The number of reservations for tomorrow night is denoted as $n$. Rooms are held until 10pm, but if a guest hasn't shown up by 10pm, ...
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How to correct zero cell counts for odds ratio calculations when variable has >2 categories

I am trying to calculate odds ratios for several univariate models with a binomial outcome. The problem is, for some of my variables, I have at least 1 zero count cell. It seems that the Haldane ...
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How would you interpret this Binomial Logit GLM? [duplicate]

I ran the binomial logit GLM which predicts whether a claim occurs in a policy or not. My estimated coefficients are as follows: Intercept: -2.68 Car Type (Saloon is base level) SUV: -0.07 Bus: 0.15 ...
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Discrepancy between binomial and beta in R?

I'm getting a result I cannot explain when using beta distribution. I've got a result which came from a binomial distribution: 2 successes in 6 trials. I would think the maximum likelihood estimator ...
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Reverse engineering Beta prior parameters from Binomial likelihood and posterior beta parameters

Suppose a friend has calculated a posterior distribution from a Beta prior and binomial likelihood, and you are interested in the prior parameters they used, but they won't give them to you. They only ...
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Survival analysis with continuous outcomes

I'm thinking of running survival analysis for continuous binomial outcome. All instances start at 0 and end at n. For example: ...
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Interpreting effect size for binomial GLM (power analysis with simr)

I am doing a power analysis to determine how many sites I need to sample (recording an animal’s presence/absence) to detect a difference between the animal's presence before and after a fire has gone ...
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Power analysis for binomial GLM with simr (having trouble changing effect size)

I am trying to determine the impact of bushfire on an animal's presence in a reserve. We already have the pre-fire data (around 200 plots were surveyed and the animal's presence/absence in the plots ...
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Counter-intuitive result from Cochran Armitage trend test and glm binomial

My question is motivated by the Q&A at How to test the increase of proportions. The question is how to test for a trend in proportion between events and non-events given an ordinal risk of 3 ...
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Can the split of an AB test be different than 50-50?

I'm running a AB testing at my company, but the split is somehow different than 50-50. Is my test still correct? Can the split be 55-45, or 60-40, and so on? When should I be worried? Sorry if the ...
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Using Offset in Binomial/Logit GLM for Exposure Years? [duplicate]

I am building a GLM Model that predicts whether there will be a claim in a certain policy or not. So target variable is either 0 or 1, so my choice of GLM was Binomial, and link function was Logit. In ...
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Overdispersion in logistic model

I'm relatively a newbie in R, and I've been trying to make a silly example of logistic regression to predict, according to Age and Sex whether someone dies of corona or not. I'm from Colombia, so my ...
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1answer
36 views

glm with log link in binomial family

I was reading this post https://r-posts.com/simulations-comparing-interaction-for-adjusted-risk-ratios-versus-adjusted-odds-ratios/ and found that the author adjusted a glm with binomial family and ...
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power analysis for binomial test

I am trying to test whether the sex ratio of some sampled individuals significantly differs from the expected sex ratio of 1. I have n= 64, of which female=34 and male=30. I ran a binomial test: ...
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1answer
87 views

Probability: Binomial data

If the true success probability for binomial data is close to 0.50, why would you expect to have less certainty with your mean parameter estimate than if the true success probability were closer to 0 ...
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59 views

No Goodness-of-Fit for Binary Responses (GLM)

In this book, p.334 (348 for pdf) it says you can model a binomial regression in a few ways: response as an observed proportion, with weights. e.g. ...
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Binomial GLMM and model predictions. Is this method correct?

I have a question concerning the statistical validity of methods. I have data about the survival probabilities of vegetative and reproductive structures of a plant along the flowering time. I am ...
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Distribution to use for when event can occur just once within 30 day period? [closed]

Let's say I have a 30-day period in which one specific event can only occur, at most, once. The probability of the event happening on Day X is likely to be front-loaded (eg. the event is more likely ...
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Can I model website conversion as a binomial distribution?

Suppose I have a website where people buy something and I've measured the conversion (calculated as buyers / visitors), and it's 0.05. I want to know what the probabilities are for the different ...
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1answer
25 views

Distribution for number of returned items per day

I am interested in estimating the percentage of returned/faulty items out of all items purchased in a shop per day (assumed that the items are returned the same day as purchased and a different number ...

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