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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Name of single sample multinomial distribution

The Binomial$(n, p)$ distribution is called "Bernoulli distribution" with parameter $p$ in the special case $n=1$. Many properties of the Binomial are derived from the fact that the sum of $n$ i.i.d. ...
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Can I use Bayes Theorem to find a conditional distribution rather than conditional probability?

I might be going about this the wrong way, but I'm trying to develop an understanding of a particular conditional value, say $P(CustomerBuysFries | CustomerBuysHamburger) = P(F|H)$. Ultimately, I want ...
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7 views

Variance of the logarithm of a binomial distributed random variable

What is the variance of $\log(1+X)$, where $X \sim Bin(n,p)$. I am looking for an approximate solutions depending on n and p. I have tried Taylor expanding the logarithm, but it didn't lead to a ...
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Estimate growth rates in a probit/logit model

I consider a situation where k different kinds of bacteria grow together in a petri dish and each kind of bacteria exhibits exponential growth, i.e. the population size over time is given by $N_i(t) = ...
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2answers
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Hypothesis test for mutually exclusive samples from a single population?

Let's say I gave 100,000 people a survey on their favorite fruit, where they can bubble in "Apple" or "Pear" (but not both). They can also leave it blank. The results are 90,000 people left it blank, ...
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Is the beta binomial with a variance equal to almost zero equal to the binomial distribution?

I was wondering whether the following holds: if I have a certain average and an almost zero variance and I use them to estimate the alpha and beta for the beta binomial distribution. Would that be ...
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15 views

Reimplement Binomial Test R-> Python

I am trying to re-implement a Binomial test in R that uses the alternative= "greater" optionin Python using scipy. Right now I am looking at ...
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28 views

click through rate stats

I have a group of 10 users. Each user receives a daily notification for one week. Ideally, each user will click on all notifications received. At the end of the week I collect the number of clicks per ...
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Understanding binomial distribution in iris recognition

I'm trying to understand, how the solid curve on the plot here was produced. The legend states that it is a binomial distribution, but as far as I know, this distribution produces integer numbers from ...
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27 views

is it ok to use binomial test for google analytics' conversion?

I have been thinking on one issue and would like to know if it is correct reasoning? In Google Analytics conversion is defined as number_of_transactions$/$number_of_sessions, one session can have ...
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30 views

How to calculate the probability of no show rate in airlines

At present I am analyzing the historical airlines data which has got the information of bookings and no shows. Now,to calculate the probability of no show rate,is it simple percentage or is there any ...
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26 views

Accounting for overdispersion in binomial glm using proportions, without quasibinomial

I am doing binomial GLM using relative abundance, for example: model<-glm(cbind(number_pres,number_abs)~Var1+Var2+Var3+Var4..., family=binomial, data=Data). My sample size is about 700, and I have ...
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Statistical comparison between binomial distributions, two groups and many trials

I have a data set with two groups. I have multiple trials with different Ns in each trial, and different numbers of trials for each group. In each trial, for each ...
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43 views

Testing for differences between populations of individuals with binomial data

So I am trying to compare between populuations and determine whether there is a difference in count based data. My data look like this: ...
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44 views

Variance of compound distribution

The binomial distribution describes the probability of $k$ 'success' events given $N$ independent trials, each with a probability $p$ of being a success. The distribution is described by the formula ...
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26 views

Minitab question about binomial probabilities [closed]

What I have tried: My first instinct was to go to Calc>Binomial distributions> Binomial to get the graph of it. 2 questions: What does the question mean it needs values less than 21? Should ...
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Binomial Logistic regression to Compare results of multiple methods to a known value

I have a "known value" (recorded by a field observer) which I want to compare several methods of data collection with to test for significant differences between methods. Methods: 2 points along a ...
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51 views

How do I include measurement errors in a Bernoulli experiment?

I would like to understand how to combine a known measurement error in a Bernoulli experiment with the confidence interval in order to calculate error bars. I am performing an experiment that has two ...
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1answer
48 views

A simple question about MAP and MLE

I recently got this simple question from a friend. But I am quite confused about it. Suppose we toss a coin $N$ times, and got heads $m$ times. Assume the binomial distribution with $p$ which is the ...
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How to address the problem of underdispersion in a binomial GLM (data in proportions)

We explored the effect of seed size, and seed-coat thickness on seed removal rates (proportion of seeds removed) and seed predation rates (proportion of seeds preyed upon)by rodents. Seed size was a ...
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Berry-Esseen bound for binomial distribution

From the Berry-Essen theorem I can deduce $$\sup_{x\in\mathbb R}\left|P\left(\frac{B(p,n)-np}{\sqrt{npq}} \le x\right) - \Phi(x)\right| \le \frac{C(p^2+q^2)}{\sqrt{npq}}$$ with $C \le 0.4748$. My ...
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350 views

Why doesn't a sample proportion also have a binomial distribution

In a binomial setting, the random variable, X, that gives the number of successes is binomially distributed. The sample proportion can then be calculated as $\frac{X}{n}$ where $n$ is your sample ...
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Relation between power and sample size in a Binomial Test?

$\beta$ (also called sensitivity or power) is a function of the sample size. It totally makes sense to me when we're performing a regression for example. The intuition is not that clear when we ...
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26 views

Analyzing binomial distributed variables

I have the following situation. A subject comes to the clinic at day 1 and is evaluated using a 10 item checklist. The sum of those 10 items is the subjects score. A intervention is performed. The ...
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29 views

Calculate the average rate of success

It sounds like a simple problem but I am unsure about the methodology I should follow. A company developed processor with a new innovative way and they tested the processors to see if they pass the ...
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37 views

LRT for one-sided Bernoulli parameter

Suppose $X_1,X_2,...,X_n$ are i.i.d. $\mathrm{Bernoulli}(\theta)$. We are interested in testing the hypotheses $$H_0:\theta\leq\theta_0$$vs. $$H_1:\theta>\theta_0$$ Show that if we use the ...
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84 views

R: prop.test - Chi-squared approximation may be incorrect

I am trying to compare the proportions of two populations, using prop.test My data is straightforward - first population is 6/26 and second is 15/171. I am trying ...
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28 views

Nominal/Categorical Data Set

I have a nominal data set of a sample(species) floating characteristic(vertical floating, horizontal floating, bottom horizontal, and etc.) over a period of time. im interested to study the most ...
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Does binomial distribution have the smallest possible variance among all “reasonable” distributions that can model binary elections?

Imagine an election where $n$ people make a binary choice: they vote for A or against it. The outcome is that $m$ people vote for A, and so A's result is $p=m/n$. If I want to model these elections, ...
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20 views

Huge increase in predicting values when removing intercept from a negative binomial model (glmmadmb function in r)

I am trying to fit a negative binomial model for predicting the intensity of deforestation (measured as a number of hectares deforested per year) from population change data, using glmmadmb function ...
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3answers
50 views

Comparing four classifiers

I have trained and tested four different classifiers, and I would now like to compare them. The classifiers have accuracies 95, 90, 81, 75. I know that there is no unbiased estimator of the variance ...
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Correct Sample Size N in a Relative A/B Test with Binomial Variates

I randomly assign users to two distinct groups and track their return rate to the website (the return rate on each day for each group is simply $\frac{Number Of ReturningUsers}{TotalUsersOnDayZero}$). ...
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Conceptual problem for binomial distribution

I'm reading this book (Implementation: How Great Expectations in Washington Are Dashed in Oakland. 1973) and they discuss how hard it is to gain agreement of actors. They set up a conceptual ...
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What are the effects of continuity correction in binomial meta-analysis in the metafor package?

The metafor package in R can be used to fit the random effects model with the exact binomial likelihood as described in Stijnen et al. (2010). The ...
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Standard Error of the ratio of Binomial variates

What's the right way to compute the Standard Error of the Mean of the ratio of two random variables that follow a binomial distribution? I asked a similar question here using Weibull distributions ...
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Confidence interval for function of the parameter - small sample size

I am trying to come up with a solution for this problem. Consider the following set of random variables: \begin{align*} X_{11},...,X_{1n_{1}}\quad &\text{i.i.d. Bernoulli(1-$e^{-\lambda_{1}}$)}\\ ...
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analytically finding the dispersion of beta distribution in multilevel bayesian model

I want to create a multilevel bayesian model of the format depicted in the in figure below. I am examining # of conversions (out of total number of exposures) in multiple subgroups. The conversion ...
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Distribution of p-values - Binomial test

I heard that under the null hypothesis the p-value distribution should be uniform. However, simulations of binomial test in MATLAB return very different-from-uniform distributions with mean larger ...
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How to process Binomial-Binomial data on SPSS for hypothesis testing?

There are 2 groups of 100 pregnant women: the first are malnourished and the second are well-nourished. A COHORT research is being done on them to determine if malnutrition is a risk factor for low ...
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Variance of binomial vs. multinomial distribution in cross-validation

Suppose we have a dataset with $N=100$ observations. We do $K$-fold cross-validation with $K=10$ and $K=100$. In the first case, the classification decisions are sampled (can I say it like this?) ...
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Fitting a GLM for binomial data in R

I am an R beginner and out of my depth! I am trying to build a model to analyse data regarding fertility in 2 populations of different levels of sexual selection(M and P), both of which have undergone ...
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Hypothesis test of 2 proportions, with $np < 5$

We are frequently conducting one-tailed hypothesis tests for 2 proportions ($H_0: p_1-p_2=0;\, H_1: p_1-p_2 > 0$). However, $p_2$ is relatively small in terms of $n, x$ and in some cases we find ...
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Is chi-squared valid in this scenario?

I'd like to know whether I am misusing Pearson's chi-squared test. And if so, what should I be doing instead. I've a game-playing program, a "bot", for a zero-sum two-player game. To improve it, many ...
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1answer
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Comparing survival times in small samples for two groups

I am working on a dataset of big cats. 18 cats have a particular antigen and the rest (58) do not. We have contact times for when blood samples were taken - so when the cats were identified as having ...
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1answer
44 views

Censored Binomial model - log likelihood

I have a dataset with multiple samples of batches of observations (e.g. one batch of 20 obs., one batch of 50 obs,, etc.). There is a probability that the batches have contaminated observations, with ...
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1answer
49 views

What measures the y-axis in stat_smooth, ggplot2 in R? [closed]

I am fairly new with logistic regression. I have a binary response. And did this plot. The binary response is: Y = 0: The student fails Y = 1: The student succeed ...
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Problem with pbinom in R (and binom.dist() in Excel)

I understand that the R-function pbinom(0, 100, 0.5, lower.tail=FALSE) returns the probability of getting 0 or more heads in 100 trials. R gives the correct ...
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Beta-binomial logistic regression model for binomial data with small samples

I have fitted a nonlinear beta-binomial logistic regression model on data y_i: y_i ~ beta-binom(n_i,mu_i,\Phi) where mu_i = exp(\eta_i)/(1+exp(\eta_i)) , and \eta_i=\beta_0+\beta_1/(1+exp(\beta_2x_i ...
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Bivariate distribution: beta and binomial

Consider a pair of RVs $X$ and $Y$, with the following conditional distributions: $$X | Y=y \sim Binom(L, y)$$ $$Y | X=x \sim Beta(\alpha + x, \nu)$$ where $L$, $\alpha$, and $\nu$; are all ...