Questions tagged [binomial]

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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7 views

Statistical test for boolean value groups

Intro This question is somewhat of a prequel to this one - but can be seen also as a standalone! I have two distinct populations/measurements of boolean values: $\{x_i\}_{i=1}^{m_1},x_i \in \{0,1\},|...
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Likelihood function of a binomial distribution [closed]

Why isn`t the likelihood function of binomial distribution (n! / (yi! * (n - yi)!)) p^(yi) * (1-p)^(n-yi) for fixed n? It is rather defined in literature as PMF of the binomial distribution; (n! / (y! ...
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Use stirling's formula to prove central limit theorem for binomial random variables [migrated]

First I must show $${n \choose k} p^k q^{n-k} \sim \frac{1}{\sqrt{2\pi n p q}}e^{-\frac{(k-np)^2}{2npq}}?$$ How do I do this? I know that Stirling's formula says that as $$n \rightarrow \infty.$$, $$...
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Convert Bernoulli random variable to Uniform distribution [closed]

Given a function randBinomial(p) that return 0 with probability p=0.3 and 1 with probability 0.7, use that function and only that function to return Uniform distribution U[0,6]
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What's wrong with my binomial logistic regression model please? (SPSS) [closed]

I am running a binary logistic regression in SPSS (standard, no stepwise) containing 20 predictors (binary and continuous) and have the following problems: 1) it correctly classifies ~the same % as ...
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Should bootstrapping and collecting sample means from a series of binomial distributions result in standard normal?

I’m trying to better understand several statistical concepts (bootstrapping, central limit theorem, and confidence intervals) by applying them to a binomial distribution (you can think of it as a coin ...
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Deriving likelihood function $\prod_{i=1}^n p^{x_i} (1-p)^{1-x_i}$ from $n$ independent Bernoulli experiments

I am studying this answer, by user kjetil b halvorsen, on likelihood functions. He says the following: We model $n$ independent Bernoulli experiments, leading to data $X_1, \dots, X_n$, each with a ...
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Application of Bayes' theorem: $f(\theta \vert x) = \frac{\theta^x(1 - \theta)^{n - x}}{\int_0^1 u^x(1 - u)^{n - x} du}$

I am currently studying the textbook In All Likelihood -- Statistical Modelling and Inference Using Likelihood by Yudi Pawitan. Section Inverse probability: the Bayesians of chapter 1 says the ...
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How to implement the estimation of parameters in negative binomial distribution in python?

Assuming the negative binomial distribution, How can I implement the estimation to parameters(r & p) especially by MLE? Which function or package should I use? scipy.stats, sympy?
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Unclear explanation of Bayes theorem

I am currently studying the textbook In All Likelihood -- Statistical Modelling and Inference Using Likelihood by Yudi Pawitan. Section Inverse probability: the Bayesians of chapter 1 says the ...
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1answer
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Discrepancy between example using the binomial distribution and binomial probability mass function definition

When studying likelihoods, I was presented with the following example: A drug is given to $n$ patients. We observe $y_1, \dots, y_n$ where $y_i = 1$ if the $i$th patient is cured and $0$ otherwise. ...
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Is it necessary to simulate unbiased coin in using frequentist approach for determining if coin is unbiased?

I’m trying to determine the best way to detect if a coin is unbiased, given some desired alpha. I understand basic probability/statistical inferencing, but there’s some information out there that ...
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Reciprocal of a binomial random variable

A production line produces faulty items independently at random with probability p. (a) Let X be the number of faulty items in a batch of 10. What is the distribution of X, and what is P(X = ...
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R: Need some help on generalized linear mixed models with binomial data

I would like to find out how the probability of tree-microhabitat occurrence is related to the age of a tree and how is this relationship influenced by KKT and Tree species. Here is an example of my ...
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p-value of 4 observations in 5 trials with one-sided hypothesis p<=0.8

This should be trivial. But when I evaluate the p-value for 4 observations in 5 binomial trials for a one sided test/hypothesis H0: p<=0.8, H_a: p>0.8 In scipy notation: ...
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23 views

Method to test hypothesis with limited data and rare events

I have simplified my problem below. Let's say you have 4 areas: A, B, C and D. Areas are either contaminated or not contaminated. Area A is contaminated. After some time area B is contaminated and ...
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1answer
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Intuition behind Method of Moments estimators of Binomial distribution

The method of moments estimators of the binomial distributions ($x \sim Binom(n, p)$) are a bit weird... I got $\hat p = \bar x + 1 - \frac{\sum x_i^2}{\sum x_i}$ and $\hat n = \frac{\bar x}{\hat p}$. ...
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Can most test contexts in marketing analytics be classified as a binomial distribution?

I've been looking at A/B tests in the context of digital marketing campaigns and am wondering what are the implications of classifying most A/B tests as a binomial distribution and conducting a ...
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31 views

Using a randomization to compare frequencies in two groups?

I have a dataset of males and females and whether they dispersed (yes = 1). For example: Male 0 Male 0 Male 0 Male 0 Male 0 Female 0 Female 1 Female 0 I'm interested in performing ...
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Predicted probabilities very close to 0 and 1 in GLM model

I've added new attributes to the binary GLM model. AUC climbed to 98%, logistic loss decreased to 0.45. Training set has ~50 cases. I can see that predicted probabilities are extremely close to 0 and ...
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Calculate a binomial in Python to determine the probability

Calculate a binomial in Python to determine the probability of getting: 7, 8, 9, 10, 11, 12, or 13 low‐birthweight babies in 100 deliveries, if the probability of this outcome is 0.1. Arrange the ...
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Calculate precision with constant sample size

Could somebody please help me to understend the following table? Is this a precision estimate for a given sample size? My colleage said that for this study, there is no formal sample size calculation,...
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adjusted binomial test with correlation

I am using this binomial test: https://stat.ethz.ch/R-manual/R-devel/library/stats/html/binom.test.html Are you aware of an implementation of an adjusted binomial test which takes into account ...
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38 views

Should I use Binomial, Poisson or Gamma distributions? With or without a log link?

I want to run a GLM to answer a few questions about differences in diet between sex and calendar year. Questions: Does frequency of occurrence (FO) of pieces eaten differ between sex or year? Does ...
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Gibbs Sampling for Order Restricted Bayesian Inference

I am trying to learn Gibbs Sampling for Bayesian Inference, I am very confused about the following setting. Suppose we observe $X :=(x_1 , \dots, x_N)$ where $x_i $ is binomially distributed ...
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Quasi-binomial GLM in R

I'd like some advice on data I'm analyzing from a factorial-design study in which each sample is a count of 200 urchin eggs that were exposed to various types and concentrations of pollutants, and for ...
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1answer
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How to compare two different coin flip distributions together?

There are two coins. With each of them we do the following steps: Flip the coins for n consecutive times Assign the number of all observed heads to H variable Replicate the experiment over t trails ...
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Beta regression or logistic regression with an offset term?

I have a dependent variable (DV) that is a proportion that is bounded by [0,1). Initially I was considering using a beta regression to model the relationship between this proportion and two other ...
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313 views

Interpreting a generalised linear mixed model with binomial data

I have a generalised linear mixed model with binomial response data, the model: ...
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38 views

Binomial distibution with mean 0

I give the following context. Test hypothesis $H_0:p=p_o$ for Bernoulli distributed random variable $X$, with parameter $p$ and samples $X_i$. For estimate $\hat{p}=\frac{1}{n}\sum_{k=1}^n X_i$, $n\...
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Confused about meaning of subject-specific coefficients in a binomial generalised mixed-effects model

In A Comparison of Cluster-Specific and Population-Averaged Approaches for Analyzing Correlated Binary Data, Neuhas, Kalbfleisch, and Hauck state: "With the cluster-specific approach, the probability ...
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Does the 10% condition apply to geometric distributions?

I know that the 10% condition is required to assume independence in binomial settings. However, in a geometric setting where there is no fixed n-value, how would one determine independence? I am a ...
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elementary statistics: compare binomial to normal distributions

Thank you for your help. I want to compare binomial and normal distributions to prove to myself (numerically) how binomial distributions approach normal distributions as n increases. I know books say ...
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How to identify the most difficult cases for classification model of a given type?

I want to build a binary classification model (GLM or GBM) for a small dataset (~100 cases). I would like to find cases that generally have the highest prediction error for the selected model type ...
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2answers
31 views

Decision making with binomial probability

This is an example given in the book . I have attached the snippet of the problem. I can infer straightaway that when 5 of 20 drives i.e., 25% require repairs within first year , than we can reject ...
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How to transform observations between different binomial distributions?

Context I am an instructor and I am trying to grade on a curve -- but using a more rigorous mathematical approach than other quick ways I've seen so far. (I'm also interested in this purely ...
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How many rejections in the observations are needed to reject the null hypothesis in a two-tailed test?

I am new to statistics. I have some basic questions to ask. Suppose we flip a coin for 500 times, we repeat the coin flipping trail for 1000 times and the null hypothesis is: The probability of ...
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Can I use a residual variable (from a binary variable) as response variable in binomial glmm or glm?

I'm working on Rstudio and I have a question about residues in a binomial glm's case. I used a glm to correct my response variable (germination (ger_b), encode 0, 1) by the light, because this ...
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What is the correct way of accepting the null hypothesis in a coin flip simulation program?

I am new to statistics so please bear with my question. There are some similar questions to mine but I didn't get the clear answer after reading them. I have a program that simulates the coin tossing ...
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1answer
59 views

Buffon's Needle problem

So I'm working through some computational stats stuff from a free pdf of a book. Specifically I'm looking at their take on the classic Buffon's needle problem. The question has a theoretical part and ...
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Correlation of a poisson RV and binomial RV

My problem is something like this problem We have $ X = Pois (\lambda)$ and $Y|X = binom (X , p)$ Where p is a known constant. And I want to calculate the correlation of $X$ and $Y$. I read the ...
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Reparameterize b(K,pi) in terms of theta

Question: $X_1, ... , X_n$ follows a binomial distribution with parameters K and 0 < $\pi\ <1.$ Use properties of Regular Exponential Class of distributions to show that the sample total $T = \...
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Obtaining valid win probabilities from contest data using a binomial model

I conducted an enclosure experiment on lizards where I recorded contest outcome for every male-male combat. We had three morphs of lizards (o, w, y) in each enclosure. I am interested in obtaining ...
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Errors if running multiple logistic models with same predictors but different dependent variables?

I have a number of predictors and dependent variables that I intend to run with logistic regression. The DVs are binary and IVs are binary and ordinal. My question is, if I run multiple models with ...
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1answer
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Binomial GLMM (GLMER) with proportions in unbalanced, observational panel data: nesting issues and errors

Thanks in advance. I am new to mixed models and having several doubts about a mixed model (lme4's glmer, binomial) with multiple levels, measuring a proportion [0,1] in three time periods. My data ...
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1answer
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Seemingly arbitrary upper bound on correlation between two binomials

I know I'm doing something wrong, but I cannot find what it is, although it's a rather simple deduction. The context is genotypes as binomial random variables, but I managed to express the problem in ...
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Comparing conversion rate in A/B testing

I have a website, and I want to see if offering a 5% or a 10% discount in an advertisement increases the click-through rate. Essentially an A/B test but with 2 alternatives, so an A/B/C test. In the ...
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Binomial Distribution:equivalency between the average and proportion?

Another user and I are having a debate regarding properties of a binomial distribution, most notably the relationship between the proportion and the mean. The central prompt is in quotations: “I ...
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2answers
271 views

Poisson Distribution vs Binomial Distribution

I have a specific problem here. It is stated as: "Assume that 30% of students in a university take public transportation daily to commute to their college. Suppose 10 of the students are randomly ...
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How to make binomial regression when some groups have 0 variance (using R)? [duplicate]

Problem: Response is binary (1/0) and some treatment combinations are so inefficient that all replicates in that group = 0 while some are so efficient that all replicates in that group = 1. Those ...

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