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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Simulating potential outcomes with a binary outcome

I want to create some simple simulations of potential outcomes to explore issues of confounding. I start with a binary confounder X and a binary treatment A. When my outcome is continuous, I can ...
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How to adjust for exposure time in a binomial model

I have several binomial (logit) models that predict the probability of various binary outcomes (e.g., incurring any costs for health care treatment, having a chronic disease). My case and control ...
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Relation between binomial distribution and multinomial distribution?

I am learning multinomial distribution. Given that $$\left\{ \begin{array}{l}{\text{a bowl of chips are labelled }}i{\text{ }}\left( {i = 1, \cdots ,k} \right)\\{\theta _i} = {\text{proportion of chip ...
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Spatial Binomial Probability (Darts Question)

Suppose a dart board divided into four quadrants and suppose $N$ darts are thrown with some unknown probability distribution. Let $p_1$ be the probability the darts fall in the two upper quadrants, $...
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Checking a GLM model using plots, Hoslem test and AIC

I am testing a GLM model from a set of categorical and continuous variables on the incidence of an event. I have first included all variables, then checked for co-linearity. Then did a step-down ...
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Interpreting binomial glm model output, what is the estimate?

I am using regression models for the first time in R. Currently using the function summary()for the glm output. I have three variables I've put into my model ...
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Should I use Chi-squared or exact binomial test?

I am testing for the difference in 30-day mortality between an exposure group and a non-exposure group. The contingency table: Taking drug A Dead at 30 days post-op Alive at 30 days post-op Yes 3 25 ...
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Test Hypothesis given 4 Binomial Experiments

I am conducting an experiment to find out whether wearing a pink pullover as a male is perceived as more uncommon than as a female. For this purpose I am conducting a Bernoulli Experiment in 4 ...
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Do we have to check heteroscedasticity when estimating quasibinomial model?

As we all know we are not interested in checking heteroscedasticity when estimating logit model when our variable is binary (taking only values 0 and 1). However do we also don't have to test ...
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How to specify that I have both independent and repeated measures predictor variables in my glmer model?

I am having a little bit of trouble wrapping my head around how to specify my glmer model. My design is as follows: y is a binomial (Bernoulli) response variable x1 is a categorical (factor) ...
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AB-Testing on Website: Binomial Test vs Chi2 or Z-Test

I have data from a AB-Test on a website: Version A Version B #Visitors 10010 9912 #Conversion 320 275 I want to test the null hypothesis that the difference in conversion is due to chance. While ...
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How to find the z score value of a point along a Wilson distribution

First I will describe the problem I am trying to solve, then I will explain how it results in the initial question (title of the post) I have a distribution, call it $A$, estimated based off some ...
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Statistical significance of assumed underlying binomial distribution for surveyed data

Lets say we have we have surveyed party preferences data for men/women. ...
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Distribution of Product of Two Binomial Variables

Related to Probability mass function of product of two binomial variables I am doing a Power Analysis for Sample Size determination. I have two binomial distributions: ...
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Confusing binomial GLM output: highly significant, but with no positive classifications

I try to investigate the influence from personal traits on drug use. I have 3 different classifications, to define if someone is a user or not. One formula I used is this (cocaine contains only 0 and ...
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Generalize from Binomial to Multinomial

Trying to find a generic formula for the probability of N players out of P players picking the same value from a dice with D sides. i.e. If we have 3 players with 3 sided dice, you have 3/27 ...
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Minimum sample size in binomial distribution [duplicate]

I have $2$ binomial distributions, $B_1(100, 0.2)$ and $B_2(n, 0.15)$ taken before and after 'some' change in item selection. What is the smallest sample of items $n$ that must be taken in order for ...
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Min sample size in binomial distribution [closed]

I am currently stuck on a prep question. I have $2$ binomial distributions, $B_1(100, 0.2)$ and $B_2(n, 0.15)$ taken before and after 'some' change in item selection. What is the smallest sample of ...
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Distribution for low probability events

I am quite new to statistics, learning on my own, please be kind :) I have process that should be viewed as Binomial distribution. It is PASS/FAIL type of process, basicly coin toss but with occurence ...
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Binomial distribution vs. Discrete uniform distribution. vs. randomly selecting

I have an array of $n$ non-negative integers where each element can be randomly (uniformly) selected with repetitions from all the integers between 0 and $m$ (with $m>n$). So the probability of ...
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Discrete Probability Density that is Monotonically Decreasing as K Increases and is 0 at K=N+1

My knowledge of distributions is limited, so I apologize beforehand for what may be a silly question. I am looking for a discrete probability distribution with domain $\{1,2,...,N\}$ that satisfies ...
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Approximate probability of minimum n such that the sum of n Bernoulli random variables is greater or equal to 1000 [duplicate]

Let $X_i$, $1 \le i \le N$ be iid Bernoulli random variables with $P(X_i = 1) = 0,92$. Let $N = min\{n: \sum_{i=1}^{n} X_i \ge 1000\}$. What is the approximate probability of $N$ being greater than ...
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dbinom(x, N, phat) in R returns “NaNs produced”. How can I solve this?

Hope I find you well, and happy new year! I have a little problem with R. I just started using it for university and I'm trying to find the binomial distribution law using the CL column of the crabs ...
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Is $\mathrm{binomial}(n, p)$ family both full and curved for $n$ fixed?

Let $n$ be a fixed positive integer. The binomial$(n, p)$ family is given by $$f(x|p)=\tbinom{n}{x}p^x(1-p)^{n-x}\tag{1}.$$ We may rewrite (1) as $$f(x|p)=\tbinom{n}{x}(1-p)^n\exp\left[x\log\frac{p}{1-...
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Probability of sequence of samples from A being more likely in B

I am trying to solve a problem, whereas I have two discrete and finite probability distributions, $A$ and $B$, over the same space. A sequence of observation of size $k$ is sampled from $A$: $(o_1, ...
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How is this formula for variance derived?

There's a formula for the variance of the traffic flow between A and B, calculated from sample data, quoted in the UK's Traffic Appraisal Manual. No proof is given and part of me really wants to know ...
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Distribution of Moving Average of Bernoulli distributed Variables

Given a series of n i.i.d. Bernoulli experiments with probability p for success each, I'd like to know the probability of crossing a threshold of somewhere having k successes over m consecutive ...
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How many must you sample with no negatives to conclude there is no negatives in the population?

If I have 1000 widgets made in my factory and I want to know that none of them are defective, how many must I sample to expect that there are no defects in the whole 1000 at 95% CL.
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Why Bootstrap CI is not recommended when Point estimate of proportion is 100% or 0%?

I'm trying to calculate the Confidence Interval (CI) for binomial proportion. The point estimate of the proportion is 100%. I first used the Bootstrapping and got a CI of [100%, 100%]. I was told it ...
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Binomial Distributions Problem

A casino customer bets on red at roulette (probability of success is 9/19). If the result is red, the client is given 3 dollars; but if she loses, she pays 3 dollars. The client plays until she has ...
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Random number (between 0 & 1; > 5 decimal places) from skewed binomial/beta-like distribution, with set mean (same as mode) and set variance

Disclaimer: I already asked this question once, however it was misunderstood and I was told by a moderator to repost it: Random number (between 0 & 1; > 5 decimal places) from binomial/beta-...
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Different z and Wald values in logistic regression analyses between SPSS and R

I am running a binomial logistic regression in R. My colleague is running the same regression in SPSS. Our DV is dichotomous and data is non-normally distributed. The IVs are a mix of categorical and ...
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Formulating hypothesis posteriorly for Binomial Testing

A common example of teaching binomial testing is viewing the results of some coin flips, seeing a total number of heads greater than the expected value, then formulating the null hypothesis that the ...
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Random number (between 0 & 1; > 5 decimal places) from binomial/beta-like distribution, with set mean (same as mode & median) and set variance

Due to misunderstandings and as per request I have rollbacked this question to this previous state. Please do not answer this question instead answer this one: Random number (between 0 & 1; > 5 ...
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1answer
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Transforming prior distribution in inference for binomial N parameter

I'm struggling with question 6 in the Exercises to Chapter 3 (page 80) of Bayesian Data Analysis by Andrew Gelman. http://www.stat.columbia.edu/~gelman/book/BDA3.pdf We have data Y modeled as ...
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Reject the claim that a sports league's regular season performance can occur by chance

For a tournament where each of $K$ teams plays each other team exactly once, what is the probability that the most number of games any team wins is $N$? The answer to this question is to create ...
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1answer
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Insufficient power from pwr.p.test

Using the pwr package, I determined the optimal sample size of 38. However, when I ran simulations using this sample size, I only get a power of 70%. What's going ...
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Colonization and extinction rates using presence absence data

I have very sparse presence/absence data that contains mostly presence information for different species across different sites and years. I am hoping to model colonization and extinction rates using ...
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Can I use AIC/BIC to compare a Poisson model to a negative Binomial model?

I would please like to enquire if it's appropriate for me to compare the fit of a Poisson vs. a negative Binomial model for my data, given that the two models are nested, i.e. the negative Binomial ...
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confidence interval for biased coin's success rate depending on number of trials

I have a biased coin where success is defined as head and the (un)known success rate is 0.75. Some clever mathematician told me about a formula: which I replicated in the R code below (it should ...
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Joint binomials [closed]

Let's say you open a bag of skittles with $n=100$ skittles and an equal likelihood of each of five colors for each piece. Upon opening it, you see that there are $x=30$ green skittles. What is the ...
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Analysis of Danish mask study data by Nassim Nicholas Taleb (binomial GLM with complete separation)

Recently, Nassim Nicholas Taleb made this post about the recent Danish mask study, a randomized controlled trial which concluded that the proportions of newly diagnosed coronavirus infections was not ...
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interpretation of the extreme point in a quadratic regression

I am doing a negative binomial regression analysis with panel data. My dependent variable is the number of patents and my independent variable the age of a CEO and its squared term. A u-test in stata ...
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Confidence vs credible interval for binomial probability

I have two related questions regarding the calculation of confidence intervals for a binomial probability and how they relate to credible intervals. (This must have appeared a thousand times- ...
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equations for the expected value and the variance for binomial

If my dataset was generated from a binomial random variable, can I provide estimates to the two parameters n (integer) and p? Using the equations for the expected value and the variance for binomial.
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Generating statistical distributions and sorting them

I am creating two distributions as shown below. ...
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Calculating the number of excursions in a Gaussian

I've written an algorithm designed to solve the following problem: An m x n array, where m and ...
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Impact of Sampling from portion of Population

So here is a scenario that I am looking at. There is a population that has a binary variable of interest. This population was collected over a year. The population was sampled and mean of that ...
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How to model binomial data when the dependent variable is LITERALLY dependent on the independent variable

I am designing an experiment where a subject makes a choice between two options ("low value" (LV) and "high value" (HV)). The subject will experience both options during a trial ...
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How to correctly use the binomial distribution for acceptance sampling?

I normaly use the hypergeometric distribution but when $n$ (sample size) is small in comparison to $N$ (batch size), I have been told by my lecturer that I need to use the binomial distribution ...

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