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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Statistical measure of international diversity

I've got a large collection of geotagged tweets, each linking to an article from a given author. For each author, I'd like to derive a number that describes how diverse is their list of tweeting ...
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Distribution of random sample of confidence intervals containing the true mean

Given 50 random samples, each of size 25, from a normal distribution with mean 20 and standard deviation 5. From each of the 50 samples, you can find a 90% confidence interval for the mean. Let Y be a ...
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The Binomial Distribution

I am trying to understand why when asked for the probability at least 1 success does it take the form 1-P(X=0) or 1-BINOM.DIST(0,1,.18,1). I am trying to understand this logic. Can you explain in such ...
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Questions about non-standard test statistic for difference of two population proportions

Background I'm considering the number of observed 'successes' $x_1$ and $x_2$ from $n_1$ and $n_2$ independent trials respectively. These counts can be considered realisations of random variables ...
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Bootstrapping probability of success: what is wrong with my method?

I have a dataset where each row represents the outcome of individual bets placed by a population of players; each row has two fields: a player identifier and the outcome of the bet (1 if the player ...
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For Y~B(11, 0.3) what is P(|Y-5| >= 3)?

I feel this is a simple problem, yet I cannot seem to solve it. Any help is greatly appreciated.
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Scaling Specificity to larger data set

Suppose I have the following 2x2 table ...
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Binomial Probability (Dice)

The throwing of a one or two is called a success. The six dice are thrown together 64 times and the frequencies of the throws with 0, 1, 2,..., 6 successes are summed over all six pairs are as ...
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Combining two estimates of p in a binomial estimation

I have an estimation problem for a binomial data. I got a sample and from that I can get an estimation. But I also have a kind of prior information about the p. But mind it, this prior is just a ...
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Binomial distribution - one-tailed

I am still struggling with a few questions regarding binomial distribution. Any help or ideas on how to solve them, would be very much appreciated!! Regards Ida N = 20. Determine the critical number ...
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Binomial distribution - coin toss

I would be really happy, if someone would explain how I solve this; Let p denote the probability for “head” in a coin toss, p = 0.5. The coin is thrown N times. What is the probability of the ...
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Evaluating a binomial (success vs. failure) glm

I'm familiar with (some) approaches to evaluating the fit (or accuracy) of a binary (logistic) model (e.g. AUC). Are there methods/approaches that are particularly well-suited for a binomial (success ...
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How to Calculate in Binomial Probability Distribution

I'm new to the Binomial Probability Distribution. I do not know how to calculate based on this formula below. Can you show me HOW to do it? ...
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cross-validate hierarchical model for binomial data that is often sparse

I have binomial data (e.g, 130 successes in 4000 trials). In many, if not most, cells of interest, there were few trials and thereby few successes (e.g., 0 successes in 35 trials, 1 successes in 18 ...
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The probability of a student getting a given question correct and the associated uncertainty (Item response theory)

I'm doing some statistics on multiple choice test scores (with item response theory, (http://en.wikipedia.org/wiki/Item_response_theory). I want to know the probability that a student with a certain ...
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Standard error of the mean for binomial dist [duplicate]

I know what intuitively what's going on but... We know that in general the standard error of the mean is $$ \sigma_\bar{X}^2 = \sigma_X^2/n $$ Right? But when I apply this to the binomial ...
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Fitting a logistic curve to cumulative data using glm()

I'm trying to fit a logistic curve to cumulative data, derived from satellite imagery. Previously, I have point observation data which were either 0s or 1s. Os being 'forest' and 1s being ...
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What are the advantages of a simulation over an exact binomial calculation?

Let's say that I want to calculate the probability of achieving more than 8 heads in 10 coin tosses. The easiest and most accurate way will be to simply use the binomial distribution and sum the ...
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Help for Binomial Distribution question

I am having issues with understanding a question on an assignment: A test for the presence of a certain disease has probability 0.05 of giving a false-positive reading and probability 0.04 of ...
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1answer
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Upper bound for asymmetry using skewness

Can the following quantity be upper bounded by the (standardized third moment) Skewness of $X$ ($\mu_3/\sigma^3$)? $$\left|\mathbb{P}(X \geq \mathbb{E}X) - \mathbb{P}(X \leq \mathbb{E}X)\right|$$ I ...
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Counterexample against binomial assumptions

The question is from a Master-level Probability Course. It is well known that the underlying assumption for the binomial distribution is that there are n independent Bernoulli trials. More ...
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Dealing with an uncertain number of trials

I've got a binomial distribution where I'm trying to figure out the probability of success (specifically, the odds of a certain event in a video game). This would be simple enough, except that I ...
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Probability of a sum of values from a number of dice rolls

4 six-sided dice are rolled independently. Compute the normal approximation with continuity correction for the probability of rolling a total of at most 6. I have arrived at a point where I got that ...
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Find MLE by combining two different experiments

I am trying to solve the following problem on an assignment. Anna has two dice. Die $F$ is fair: it rolls $1,2,3,4,5$ or $6$ with equal probability $\frac{1}{6}$. Die $D$ is dodgy: Anna suspects ...
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Hypothesis testing with multiple variables

I'm trying to understand the process behind testing both A/B site changes for statistically significant increases in conversion rate, and also how then to expand this to testing multiple variables. ...
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binomial test for over-represented kmers in biological sequences - what is the right test?

Imagine you have a long string, like a genome, and you split it up into every overlapping word of size n. This is called a kmer. ...
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Estimation probability in related binomial distribution

I have two binomial experiments with an unknown probability - But i do know that the ratio between the probability in the first experiment and the probability in the second experiment - For example I ...
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Standard error of proportions, with weighting

I have a set of experiments $i=1\dots k$ each of which performs $n_i$ binomial experiments, recording a fraction $p_i$ successes. Clearly if I trust all of the experiments equally, my estimated ...
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Using the binomial distribution to identify chance-level responses

I have a subject who was giving 2-alternative forced choice responses for a task consisting of 80 trials. For each trial, there was a 50% chance for each of the two options to be correct. This means ...
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Problem solving a simple probability exercise

I'm currently studying a Statistics course and I'm trying to solve a simple probability exercise: A production facility employs: 20 workers on the day shift 15 workers on the swing shift 10 workers ...
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Why does SAS PROC GLIMMIX give me VERY different random slopes than glmer (lme4) for a binomial glmm

I am a user more familiar with R, and have been trying to estimate random slopes (selection coefficients) for about 35 individuals over 5 years for four habitat variables. The response variable is ...
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How to sample from “biased” binomial distribution (ideally in python/numpy)

I need to sample a variable from a distribution that's like a binomial distribution except with a "bias", I'm not sure what it may be called: $p(X=k)$ is proportional to $k.B(n,p)(k)$ where $B(n,p)$ ...
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67 views

How to model a count dependent variable with upper limitation

I have a dependent variable, which have 0, 1, 2, or 3 for its value. I asked participants to choose three items and coded 1 if it is in a certain category and 0 otherwise. I add the three binary ...
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Bayesian estimation of $N$ of a binomial distribution

This question is a technical follow-up of this question. I have trouble understanding and replicating the model presented in Raftery (1988): Inference for the binomial $N$ parameter: a hierarchical ...
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Estimating $n$ and $p$ for Binomial distribution, repeated counting of partly hidden population

A brief motivation: $n$ critters live in an aquarium, where sadly they often hide in, under or behind things. When the aquarium is observed, each critter is only seen with probability $p$ ...
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Test if two binomial distributions are statistically different from each other

I have three groups of data, each with a binomial distribution (i.e. each group has elements that are either success or failure). I do not have a predicted probability of success, but instead can ...
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Identifiability in generalized linear random effect model?

Suppose I observe binary $Y_{ij}$ for $i = 1, ..., N$ and $j = 1, ..., J$ and I want to model $$\Pr(Y_{ij} = 1 \mid \lambda_{i}) = \Phi(\lambda_{ij}), \qquad [Y_{ij} \perp Y_{ij'} \mid \lambda_i]$$ ...
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Posterior distribution of proportional difference of two binomial variables

Can somebody point me in the right direction for a treatment of the following problem? I imagine this should be a fairly common problem in medical statistics... Given two binomial random variables ...
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Formula for calculating sample size for hypergeometric distribution

Suppose you have an urn with "N" marbles. All marbles are either black or white. You take a sample of size "n" without replacing them to the urn. With this one sample you would like to be able to ...
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Binomial data and PCA and cluster analysis

I have obtained responses on around 48 items measuring employer attractiveness. The goal of my analysis is to cluster respondents according to these employer attractiveness dimensions. I plan to ...
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Analytic or sample standard deviation with binomial data

I've been looking for recommendations on whether it's better to use the sample standard deviation (SD) for a binomial distribution or use the analytic SD (or variance). It's for experiments with ...
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Correcting for multiple testing on non-independent sliding windows

Question Values taken from adjecent windows in a sliding windows are corrolated. If I calculate a p-value from each window, how can I correct for the fact I have tested many windows, given that the ...
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Comparing polynomials

I've got a bunch of data on pop singers' performance on the Hot 100 charts over time, and I'm trying to compare the early part of different artists' careers. For example, I might look compare Miley ...
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Binomial random variable conditional on another one

On the Wikipedia page for the Binomial distribution, the following property is mentioned (under the related distribution section): (paraphrased) If $X\sim \text{Bin}(n,p)$ and $Y|X \sim ...
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How can I do a test for proportions when the data has been collected weekly from the same general population?

So I have a series of proportions taken weekly for 7 weeks. This is a study of which way spiders were facing. So for example, the first week, 20 spiders were facing out, and 10 were facing in. Now I ...
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Conditional on binomial question

Here goes the question from textbook: A small restaurant seats 20 diners, and is full every night. The chef knows from previous experience that 40% of the diners order steaks, so she always has 12 in ...
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Bootstrap of parameter estimates and confidence intervals (hurdle model)

Think you can help with this. I´ve run a set of candidate hurdle models on insect abundance data with pscl package for R. These models had an abundance part with a truncated negative binomial ...
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Using a binomial approach to calculate significance of multiple significance tests

I have 10 data sets with normal distributions and carrying out significance tests on each one. With this many data sets, there is a good chance that some will be significant by chance. I am going to ...
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Difference test for beta–binomial variables

Let $X \sim \textrm{Beta–Binomial}(\alpha_1, \beta_1, n)$ and $Y \sim \textrm{Beta–Binomial}(\alpha_2, \beta_2, n)$ and write $\mu_1 = \frac{\alpha_1}{\alpha_1 + \beta_1}$, $\phi_1 = \alpha_1 ...