# Questions tagged [binomial-distribution]

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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### Completeness calculation: Where does the $\sum_{i = 0}^n g(i)$ in $E_p[g(T)] = \sum_{i = 0}^n g(i) {n\choose{i}} p^i (1 - p)^{n - i}$ come from?

I have the following definition of completeness: Definition Let $Y_1, \dots, Y_n$ be an i.i.d. $f_\theta (y)$, where $\theta \in \Theta$. A statistic $T(\mathbf{Y})$ is complete if no function $g(T)$ ...
2answers
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### exact binomial test with power calculation that excludes the lower limit of a 95% CI

In a regulatory document I see the following statement and wonder how the sample size of 141 subjects is calculated: A sample size of 141 subjects provides 80% power to exclude a response rate of 12% ...
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### Is this tennis player a fraudster?

In this article Anhörig vann 270.000 kronor – tennisspelare åtalas för mutbrott it is claimed: It seemed that she intentionally hit double errors or lost points on occasions in the match so that she [...
1answer
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### Likelihood function for number of slots taken over slots available

I have a study in which I am comparing the number of outpatient visits a certain surgery experiencse in a same period in two different years; the total number of visits is a limited by the number of ...
1answer
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### What is the name and formalism of this discrete distribution? [closed]

I am searching the name of something similar to a binomial distribution, but with individual probabilities (P(1) to P(N)). I calculated (brute-forced with a script) the probability of k positive ...
1answer
58 views

### Does a Binomial converge to Poisson or Normal?

I have read the answer here. Here the distinction is that If $n\to\infty$ and $p\to0$ while $np$ approaches some positive number $\lambda,$ then the binomial distribution approaches a Poisson ...
0answers
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### Confidence interval for combined populations

I'd like to compare two approaches for calculating the confidence interval ($CI$) when estimating the mean for a sample of weighted values: The first approach is based upon the standard error of the ...
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### Deriving Gaussian from Binomial?

Just for the sake of curiosity, I've been curious if the Gaussian distribution was derived from the Binomial, or if it was found by other means, and retrospectively associated with the Binomial. ...
1answer
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### Binomial GLMM with proportions and categorical predictors

Study background My research question looks at the effect of age group (AgeGr) on gazing. Each infant was observed for 1h and signals with gazing (...
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### The tail distribution of a binomial distribution can be expressed in terms of an appropriate beta distribution function - Explanation [duplicate]

I was reading the paper: "Estimating Probabilities of Default for Low Default Portfolios" by Katja Pluto and Dirk Tasche and they mention the following: The tail distribution of a binomial ...
1answer
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### Binomial vs hypergeometric finite sampling distribution

I was reading these notes:Finite Population Sampling with Application to the Hypergeometric Distribution and I have a question just about the first two pages. The first page, they derive the variance ...
1answer
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### Binomial hypothesis test for $p_1 = p_2 = P$ without normal approximation

I was testing whether the proportion of successes from two populations is the same. It made me realize I only know how to do this with a normal approximation. In particular, I would like to solve ...
1answer
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### Hit probability of a motif in DNA sequence

I am trying to figure out expected number the occurrences of a DNA motif in a sequence. Let me first show a small example for the base case: Assume we have a DNA sequence 'TACCTG', where in every ...
1answer
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### binomial vs betareg? glm for y=ratio

https://docs.google.com/spreadsheets/d/1e_XOgTv1flSFFleHSwUJJPBzBdd9VPXRaZc2oukwtrE/edit#gid=0[data] I'm using glm to evaluate the response of mammal species to different % of forest cover. My ...
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### Distribution similar to binomial that can account for changes in variance due to sample size?

Imagine that I am measuring successes and failures where p=0.5 and sample size = n. The problem is that I know that with increasing n, the variance of the success or failure measurement also increases,...
1answer
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### Intuition or proof for combinatorial function in binomial distribution

For a the probability of a binomial distribution with n trials, the probability of k successes where Prob(success) = p is (n Choose k) * p^k * (1-p)^(n-k). I understand that we have to multiply p^k * ...
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### One-sample: difference between two proportions that are parts of the same whole

What is the sampling distribution of the difference between two proportions when they are parts of the same whole. It's relatively easy when one proportion is binomial, the one of the common ways to ...
1answer
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### Covariance between a binomial random variable and its size (number of trials) (found in the context of binomial thinning)

Assume we have a random variable $X$, and we construct another random variable $Y$ to be from a binomial distribution of size $X$ and success probability $\alpha$, i.e., $Y \sim Binom(X, \alpha)$. How ...
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### How does Pfizer justify it's Beta-Binomial model?

This is a bit of a hodge podge of different clinical trial related questions, but starting with some basics. It seems like they're defining vaccine efficacy differently depending on where you look. At ...
1answer
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### How to compare a population proportion to a probability of success of 1?

I would like to assess whether my population proportion (P1) is significantly different from a hypothesized value (P0). I would usually use a binomial test to test this hypothesis. However this time ...
0answers
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### What type of statistical test should I use?

I'm running an experiment to try and analyse how often people punish those who betray a group. We made a choose your own adventure type game and got people to play it. It simulates a secondary school. ...
1answer
38 views