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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Generalised Likelihood Models

Why would you use a re-scaled binomial distribution rather than just the standard binomial distribution as the distributional assumption in a GLM?
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rbinom() produces NA values. What's wrong?

I have to generate RV from a binomial distribution with R . I have a vector for $n$ and a vector for $p$ and for each component I have to generate a random variable. My idea was the following for ...
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Generation of random variables [migrated]

I have a problem about the generation of random variables with R . I have to generate random variables $X_{ij}$ (i=1,...,25, j=1,...,5 ) knowing that each X_ij follows a binomial distribution ...
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Maximum likelihood estimation of p in a Binomial sample

Assuming I need to find the ML estimator for p, p being the chance of success in a Binomial experiment $Bin(N,p)$, I would expect my density function to be: $$ f(y) = {{N}\choose{y}} p^y(1-p)^{N-y} ...
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Estimate probability mass function from observed samples?

This question is related to but is distinct from Estimation of probability mass function using finite samples. As in the related question, suppose we have a discrete random variable $X$ with known ...
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binomial confidence including run to run variation for overdispersion

I'm trying to determine the model to correct a confidence interval (binomial proportion for example) but to also include overdispersion affects that arise from a Run-to-Run variation. Example, case ...
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Probability distribution for a proportion based on (continuous) quantities

I have a problem related with probability distributions and parameter estimation, which comes from a real case. I would be very grateful if you could help me. Let us suppose that we have a continuous ...
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Binomial regression does not give coefficients for all IVs [duplicate]

I have a dataset with the dependent variable presence / absence (0 and 1) for a certain species. I have three categorised IV's (2 IV's with 3 categories and 1 with 2 categories). To test the response ...
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How to calculate the absolute central moment of a Binomial distribution?

There is an experiment. The coin is tossed $n$ times with $p = 0.5$. The experiment is repeated $k$ times. I need to calculate the average central moment. For example, let $n = 5$ and $k = 3$. $[0, ...
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Expectation-Maximization Algorithm for Binomial

I have a multinomial distribution with four outcomes, with a pdf: $$p(x_1,x_2,x_3,x_4)=\frac{n!}{x_1!x_2!x_3!x_4!}p_1^{x_1}p_2^{x_2}p_3^{x_3}p_4^{x_4}, \sum_{i=1}^4x_i=n, \sum_{i=1}^4p_i=1$$ The ...
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Molecules movement distribution puzzle

Let's say I have blood samples of whiteblood cells ($x$) and viruses ($v$). Space has been discretized in $LL$ spaces. They have a $p_v$ probability of interacting when found in the same space. I want ...
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Which test should I use to determine whether multiple binomial experiments results are different, with p not equal to 0.5 for all? [duplicate]

I have four subject A,B,C,D, I asked 500 students whether they like each subject, there are two choices: Yes/No. I want to test, do students have a preference for any of A/B/C/D? Originally I used ...
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Binomial data: Null Hypothesis $p = 0$ when all Sample Values are 0 - testing and power analysis

I am trying to investigate if the proportion of successes in my population can be shown to be larger than zero. Thus, $H_0: p = 0$ and $H_A: p>0$. Since $p=0$, the prop.test in R does not work, ...
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Comparing rates of success in paired groups of samples

I have $2n$ paired populations, on which I measure a rate of success, let's say $(r_{group}^i)_{group \in (0,1)}^{i \in[1,n]}$ where $r_0^i$ and $r_1^i$ are the rates of success in the $i$-th pair of ...
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Generating Binomial Random Variables with given Correlation

Suppose I know how to generate independent Binomial Random Variables. How can I generate two random variables $X$ and $Y$ such that $$X\sim \text{Bin}(8,\dfrac{2}{3}),\quad Y\sim ...
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hypergeometric vs. binomial for sales modeling

Suppose you are selling Product X. You have a customer base with $N$ people. You want to measure the "natural buying probability" (which happens because a customer sees Product X in ads), so you ...
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truncated binomial samples with GLM

We have a binomial process that yields samples of 60 trials. To save time, once 2 failures have been observed the process is reset. So if a test series hits 2 failures early, the resultant sample ...
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Non-integer Binomial test equivalent

This is probably a very basic question, but I just can't seem to find the answer elsewhere. If I want to calculate the probability of a certain number of events occurring (say 9 heads out of 20 coin ...
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appropriate binomial proportion confidence interval for repeated measures

So I have looked this up extensively and keep getting the same answer, but its because what I can find online isn't quite to the point. I want to put a confidence interval on a binomial proportion, ...
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Cox/ Binomial Regression: How to reconcile Non-significant model with significant IVs

I'm been performing some survival and regression analyses corresponding to an event of interest being death or a certain surgical procedure, namely a shunt revision for pediatric neuro-surgical ...
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How to interpret parameters of GLM with binomial family for proportions

I would like to use glm with binomial family for proportions. However, I am wondering how could I interpret the parameters that is important in my case. In binary logistic regression one can interpret ...
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How to estimate probability of $\geq$ n type I error in multiple testing comparison?

My question is about the calculation of the probability of making $\geq n$ type I error when $p$ independent statistical tests are made. I can calculate the probability of $\geq 1$ type I error with ...
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Interpreting Cox & Binomial Regression: non-significant Chi-Square values w/ significant wald statistics

Scenario A: In Cox regression, the chi square analysis of the -2 log likelihood (or the omnibus in binomial) is not significant, but some of the values of the Wald statistic corresponding to some of ...
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Is this correct?

There are 40 questions. For each question, there are 5 options of which only one option is correct. 3 points are awarded for each correct answer, and 1 mark is deducted for each wrong answer. For ...
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Ancillary statistic in exact tests

I have been reading about use of ancillary statistic in hypothesis testing. For e.g. To test variance the test statistic is chi sq distributed and is independent of variance. (Please correct me if I ...
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Binomial Distribution vs Poisson Distribution

I don't understand what context should I enable to use binomial or poisson distribution? Any pros and cons for each distribution?
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Logistic Regression: Bernoulli vs. Binomial Response Variables

I want to perform logistic regression with the following binomial response and with $X_1$ and $X_2$ as my predictors. I can present the same data as Bernoulli responses in the following format. ...
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Does this variable follow a poisson distribution or a binomial distribution?

I dance an average of 2/7 nights during a week. D = Number of nights dancing in one month/4 weeks. My first thought was Poisson, but am now unsure. Is it none of the above?
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Is a random variable Bernoulli? Is a proof available?

Suppose a die is tossed twelve times and each outcome is represented by a random variable $X_{i}$. Further define $Y_{i}$ for $i=2,...,12$ to take the value $1$ if $X_i=X_{i-1}$ and $0$ otherwise. ...
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Estimates of random effects in binomial model (lme4)

I'm simulating Bernoulli trials with a random $\text{logit}\, \theta \sim {\cal N}(\text{logit}\, \theta_0, 1^2)$ between groups and then I fit the corresponding model with the ...
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Replacing FWER corrections with binomial tests

Say I have $m$ hypotheses to test and I'd like to test them using classical hypothesis tests (i.e. with $p$ values) as part of some simultaneous inference at a confidence level of $\alpha$. Rather ...
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When to use (and not use) the rule of three

The rule of three in statistics states that if an event is binomially distributed and does not occur with in n trials the maximum chance of it occurring is approximately 3/n. Suppose we have a ...
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How to calculate odds of excess occurrences

My question is on how to determine the percentage chance of an occurrence exceeding the expected number of occurrences. For example in poker, there is a 21.77% chance of an Ace appearing on the flop ...
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On deriving the Poisson distribution from the binomial distribution

My own personal understanding of modeling the number of independent uniformly distributed events occurring in a fixed time interval, is that we can first approximate this with a binomial distribution ...
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In a Binomial Distribution Do Precision and Recall Always Cross At Prevalence

Using Precision, Recall and Prevalence as defined here: Wiki information retrieval Precision = |{relevant document} Intersection {retrieved documents}| / |{retrieved documents}| Recall = ...
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Power analysis for binomial test via simulation

Suppose a gene is mutated in 30% of the samples. I want plot the number of samples required to see 30% of them mutated at various level of power. I want to do this through a simulation so I ...
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Binomial distribution: calculating the probability of a given number of successes with R

I'm a bit lost here, could someone please enlighten me? Let's say we have this simple example: A 2005 survey found that 7% of teenagers (ages 13 to 17) suffer from an extreme fear of spiders ...
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What is the relationship between zero-inflated binomial and Bin(n,p) distribution?

Hi just could anyone explain the relationship between zero-inflated binomial and $\text{Bin}(n,p)$ distribution? I think zero-inflated binomial should be a kind of mixture and $\text{Bin}(n,p)$ and ...
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Are different p-values for chi-squared and z test expected for testing difference in proportions?

I'm trying to test the difference in proportions using the z test method and chi-squared method, but am getting very different answers. Is that normal? My data: ...
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R: glm function with family = “binomial” and “weight” specification

I am very confused with how weight works in glm with family="binomial". In my understanding, the likelihood of the glm with family = "binomial" is specified as follows: $$ f(y) = {n\choose{ny}} ...
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Binomial Question with two probabilities

What we do if we were to figure out the probability of lets say, to pass a certain round of a quiz when there are 2 probabilities involved? Specifically, If in a round there were 2 Multiple choice ...
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Confidence Intervals for Non-normal data?

I have a dataset where the response is the number of successes and I have two factor variables A, B (A has 6 levels and B has 4 levels) and a quantitative variable H (H is hours so it is ...
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Testing Whether a Binomial Distribution Fits Data

I have a sample from a discrete distribution as such: Type: 0 1 2 3 4 5 Occurrences: 88 12 52 43 21 5 My task is to test whether ...
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(Failure) probability calculation

I am working on mortality in 12 hospitals performing cardiac surgery in babies. The dataset is available here: Surg dataset. The dataset is structured in this way: ...
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R binomial family with identity link

I want to fit a linear model by R with family=binomial(link="identity"), however, binomial family do not have identity link. What should I do?
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Binomial distribution [closed]

folks! The problems is Suppose you can make free throws at a 70% rate. Let X be the number of free throws you make in 20 tries. Model this with a binomial distribution: 1)?= E[X] 2)?=Var[X] ...
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Accounting for initial values of reponse variable in binomial GLM

R v.3.1.0. Mac OSX 10.9.5. Can somebody please recommend a method to account for initial values of a response variable in binomial GLMM? I am designing an ecological experiment, and am having a hard ...
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What is the reason for this discrepancy between confidence level and probability?

I ran the following R code: library(Hmisc) binconf(x=1, n=70) # PointEst Lower Upper # 0.01428571 0.0007327613 0.07658187 Which is the ...
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The probability of m out of K things being wrong with an error of ɛ

I have a homework question about a machine-learning algorithm that uses ensemble learning with simple majority voting. Assuming we have K hypotheses, each with an error ɛ, the question asks us to ...
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Which distribution to use for a probability problem?

In a food processing plant, on average, 2 packaging machines breakdown per week. I let x be the number of processing machine breakdowns in a week. So x is Poisson(2), but one part of the question ...