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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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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How do i input binary data correctly for generalised linear models in SPSS [on hold]

I am looking at which habitat variables might be explaining the presence of an organism. I'm completely hopeless at maths and therefore statistics is even worse for me. The data set i have is pretty ...
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2answers
121 views

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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656 views

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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Normal Approximation to the binomial distribution and probabilities [closed]

Based on long experience, an airline found that about 7% of the people making reservations on a flight from Miami to Denver do not show up for the flight. Suppose the airline overbooks this flight by ...
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10 views

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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32 views

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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18 views

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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56 views

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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93 views

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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23 views

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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1answer
47 views

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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34 views

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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Whether the following problem represents a Bernoulli trial (binomial)

I have the following problem but I am having problem finding the correct answer: A manufacturer recalls a doll because about 5% have buttons that are not properly attached. Customers return 43 of ...
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1answer
19 views

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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37 views

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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31 views

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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56 views

(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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1answer
62 views

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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1answer
61 views

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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199 views

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 ...
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Statistically prove that answers to questionnaire are not correlated to questions

I have a questionnaire of 4 "yes-no" questions: A1,A2,B1,B2. The correct answer for A1 and A2 is "yes", and the correct answer for B1 and B2 is "no". I need to statistically show the fact that ...
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Estimating variance of a function of multiple random variables?

What are some strategies for estimating the variance of a statistic that is an arbitrary function of multiple random variables? I am familiar with the Delta method which uses asymptotics to estimate ...
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2answers
40 views

Testing the difference between two parameter estimates in binomial GLM

There are some related posts on this issue, but no answers actually demonstrate the mechanics of how to accomplish the task that I could find. I want to compare two parameter estimates in a binomial ...
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63 views

Significance in beta regression and glm binomial

While performing betaregression using betareg R package I noticed that the terms in my model are often significant, even with very small sample sizes. I tried the same model using glm with binomial ...
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2answers
86 views

Compare two binomials with unequal groups of trials

I'm attempting to determine if store B is 'better' than store A. Let's say that the two stores are identical in every way except for the sales assistants. I'd like to determine if one store makes more ...
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39 views

Conditional distribution function of sum of correlated Bernoulli variables

Let $X_i$ be a Bernoulli variable with probability $p$ for $i=1,...,N$. Hence $\sum_i X_i$ is binomial and approximately normal$(p,(1-p)p/n)$ for large $N$ The conditional probability distribution of ...
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Determining preference using a binomial test. Is this the right way to go?

Let's say you are running a blind essay on preference of a new product. You make people taste two different drinks and record their response. They prefer A and you record it as a failure in a ...
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Can I run a multivariate quasi-binomial analysis of proportion data?

I am trying to best analyse a set of foraging ecology data with >10 behaviour categories (DVs) and 3 levels of IV (season, sex, age). The time which an animal spent engaged in a behaviour was recorded ...
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28 views

Are sensitivity and specificity complement of each other?

Sensitivity : probability that a person with the condition will be classified in one's study as having the condition. ...
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94 views

Arcsin CI for proportion

I'm trying to replicate a study. I have 165 observations of a proportion variable (the distribution is skewed to the right as many proportions are low). I need to report the CI. I've applied ...
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Is there a formula for a general form of the coupon collector problem?

I stumbled across the coupon collectors problem and was trying to work out a formula for a generalization. If there are N distinct objects and you want to collect at least k copies of each of any m ...
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SPSS regression discrete number of outcomes

Patients were asked whether they experienced 6 different health consequences following a procedure. As well as looking at the predictors for each individual health consequence, I am also interested in ...
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Derivation of cumulative Binomial Distribution expression

I have a binomial distribution, with Random Variable Y and n trials. r is an integer. How can I show that P(Y ≥ r) = P(Y ≤ n − r)? I think it involves using the binomial theorem. I have tried taking ...
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35 views

calculating the statistical significance of overrepresentation of a substring in a string

I have a sequence of characters in a long string like this 'ATCGCGCGCGATCGACGCGTACGTCGGATCTA.....' And I know that for example the substring 'ATCG' has been ...
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1answer
62 views

Why not use always a binomial exact test to compare two proportions instead of chi square?

I am trying to figure out what test I should use in the following scenario: I know that there is a lot of room for improvement in a specific area at work - being extremely critical, let's say that ...
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Laplace approximation for binomial distribution in matlab

i using bionrnd() function to generate a random vector and Laplace approximation formula to approximate the binomial distribution. but Laplace histogram dose not ...
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72 views

Is there a way to do a statistical test if an independent variable has only 1 level?

I have a repeated measures design in which I tested multiple individuals with three different sounds (playbacks). The playbacks were 20 seconds in length and I recorded 1) how individuals responded ...
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1answer
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Assessing fit of binomial glmer() in R with only categorical predictors

I am trying to validate a mixed effects logit regression model with a categorical dependent variable and categorical predictor variables - I have nothing that is continuous. One of my predictor ...
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1answer
26 views

Developing probability distributions

An event occurs, and after this event has occurred there is a set of conclusions which can be drawn. All of these conclusions have results which are distinct. I am trying to keep this as general as ...
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1answer
51 views

Difficulty with power analysis

I need to estimate sample size for an experiment but I am not very knowledgeable about power analysis. In my experiment, I am asking if a user can notice the two possible states of a system. I ...
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28 views

Uniformly Most Poweful Hypothesis test for the difference between two means

I have data for two groups, $G_1$ of n trials and $G_2$ of m trials, of which datasets $x_1$ and $x_2$ have been collected. These can be binomially distributed, $X_1$ ~ B(n,p), $X_2$ ~ B(m,q). I ...
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How to tell the probability of failure if there were no failures?

I was wondering if there is a way to tell the probability of something failing (a product) if we have 100,000 products in the field for 1 year and with no failures? What is the probability that one of ...
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What is the best approach to measuring significance in two binomial distributions?

I have been using the Wilson score interval to determine whether the registration rate from two different website flows are significantly different. I want to see if there are suggestions for better ...
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Asymptotic distribution of the max (min) of IID binomial variables

I would like to know the limiting distribution when $k \uparrow \infty$ and $k/n \rightarrow \lambda$ of $$ \max(X_1, \ldots, X_k), \text{ where $X_i$ are IID $B(n,p)$}.$$ This is most likely a ...