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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191 views

Interaction plot between categorical and quadratic continuous variable

I ran a GLMM model with a binomial response to analyse bear presence at feeding sites (0 = absent, 1 = present) within two years. My code is: ...
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321 views

Are there better estimators of misclassification error than the fraction of misclassified test points?

Assume we train a binary classification model using the training set. Also assume that the model returns an estimate of the probability of success $\hat f(x)$ for every feature vector $x$ and was ...
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Linear mixed effect model with fractional/proportional outcome: choosing between binomial and beta

I'm looking to run a linear mixed effect model using lme4, where my dependent variable one_syllable_words / total_words_generated is a proportion and my random ...
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1k views

Use Chi-Squared or Binomial Test if Distribution is not Known?

Suppose you have a set of data (eg. [a, b, a, a, b, b, etc.]), and you have the suspicion that the set of data follows the binomial distribution. Your Null Hypothesis is: The probability of success ...
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486 views

Election fraud detection: the statistics of Quick Count

I’m reading the book Quick Count and Election Observation (chapter 5). I’m interested in understanding the statistics used in Quick Counts. Quick Counts is a methodology for verifying official ...
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446 views

Hypothesis testing for binomial distribution: a simple real-life case

I'm refreshing (or maybe just acquiring) some stats skills, and I have a real-life situation, probably very simple since it's quite close to a typical example from stats courses, that I would like to ...
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210 views

Sample size determination contradiction

I'm struggling with a contradiction when trying to determine a sample size when proportion is small. If I use binomial formula: $n = p(1-p)z^2/ME^2$ then the smaller the proportion - the smaller ...
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292 views

Hierarchical model: question on frequentist estimation

I am interested in understanding the differences between Bayesian and Frequentist estimation in the context of hierarchical models. Consider $n$ subjects, where for subject $i$ there are $k_i$ ...
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174 views

Simple $\chi^2$ test question

I have the following question which seems extremely easy, but the way the data are set up is causing me some uncertainty: I plan to solve this problem through finding the maximum likelihood estimate ...
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134 views

Joint distribution of column sums when row sums are fixed

Suppose I have an $m$ by $n$ table $X_{ij} \in \{0,1\}$, where in each row, $r$ randomly chosen entries are set to 1 (the rest are 0), i.e. $\sum_j X_{ij}=r$. I know that e.g. the column sum $\sum_i ...
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Binomial mid-p value

I've been under the impression that the mid-$p$ values generally control the Type I error, and consequently confidence intervals based on mid-$p$ values control the coverage. However I have checked ...
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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 ...
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Modeling binomial outcomes with repeated measures

I'm looking at patterns of a particular injury within individuals and how they vary by age and sex. For each of 1365 individuals I have four locations each of which may be positive for this injury. ...
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Beta-binomial distribution for scaled and translated Beta

Recall, that a binomial distribution in which the probability of success at each trial is randomly drawn from a beta distribution results in the so called beta-binomial distribution. One can calculate ...
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73 views

binomial glm where number of trials is also a predictor

I am modeling the probability of success $p_i$ under a binomial framework. In fact I am actually modeling $x_i \sim Bin\left( n_i, p_i\right)$ being the number of trial varying along each observation. ...
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959 views

Overdispersion in a binomial GLMER model

I'm having trouble accounting for overdispersion in a binomial GLMER (lme4 package) - I'd read through other posts on the topic but haven't found anything that solves my problem. I tried adding an ...
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330 views

How Negative Binomial Distribution and negative bionomial regression can be used to sales forecast?

My first question here. Due to the improper inventory management we seem to have dispersed sales, and the stores are unable to meet the demand because items are being out of stock. There are so much ...
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422 views

What is the equivalent to a binomial test for more than two populations?

I have the minor allele frequencies for three populations for a given SNP (location in the genome). ...
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548 views

Multiple imputation of glm binomial size parameter

Suppose we have a generalized linear model with a binomial response $y_i\sim \mathrm{bin}(n_i,p_i)$ where $p_i$ is determined by the linear predictor in the usual way via some link function. Is there ...
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913 views

Including seasons and months into GLMM: should they be crossed or nested effects?

I have collected data from five consecutive fishing seasons (five factor levels). Each fishing season has five months within (five factor levels). Considering that I have a temporal correlation in my ...
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333 views

The marginals of a truncated multinomial are truncated binomials?

The multinomial distribution for a vector $\vec x$ of non-negative integers assigns a probability of: $$f(\vec x) = n!\prod_i p_i^{x_i}/x_i!$$ to every vector $\vec x$ of non-negative integers in ...
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1answer
97 views

Bayesian inference with unequal sampling

I have a "two-column" data set, with a multi-class categorical variable A, and two-class variable B. It is assumed that each observation is independent. For each category of variable $A$, I want to ...
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531 views

Theoretical justification of choice for confidence interval exact method for the success probability parameter of negative binomial variable?

I have a computer experiment that runs the Bernoulli series with unknown probability $p$ of success. The experiment terminates when $m$ failures are observed. So, the unknown parameter $p$ has the ...
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How to calculate standard errors of a non-linear model prediction?

I'm trying to understand how to show the prediction error of a model fit in R using the non-linear least squares function nls. Although there is an argument ...
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179 views

Non-parametric estimators for time-varying binomial proportion

I have a bunch of count data associated with time intervals (potentially overlapping and of variable lengths), say $(s_i, t_i, n_i, N_i)$ where $N_i$ is a count of the total number of events ...
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1answer
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How to analyse a continuous response having a bimodal distribution?

I am investigating unconscious racial prejudice as a predictor for guilty or not guilty judgements (Using SPSS). I have a continuous variable for unconscious racial prejudice (higher numbers equal ...
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How many orders will be placed on average until stock runs out, given a probability that the customer will find the item they want?

Let there be 500 units of stock $s$ of diverse items in a store. Customers arrive one by one and, for every given item, there is a likelihood $m$ of 5% that it is precisely the item that the customer ...
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73 views

Confidence intervals for binomial generalised linear model with cauchit link function

The correct way to calculate a confidence interval (CI) for a generalised linear model (GLM) and avoid the problems of normal approximation intervals has been adequately discussed by Gavin Simpson ...
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1answer
26 views

Distribution for low probability events

I am quite new to statistics, learning on my own, please be kind :) I have process that should be viewed as Binomial distribution. It is PASS/FAIL type of process, basicly coin toss but with occurence ...
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Counter-intuitive result from Cochran Armitage trend test and glm binomial

My question is motivated by the Q&A at How to test the increase of proportions. The question is how to test for a trend in proportion between events and non-events given an ordinal risk of 3 ...
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1answer
46 views

Logistic regression with binomial independent variable

I have a table of observations, with three columns --- (a) class labels (can be 0 or 1), (b) counts of successes (out of a certain number of Bernoulli trials) and, (c) numbers of Bernoulli trials. I ...
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62 views

Literature request: (in)appropriateness of negative binomial for count data with an upper bound

I conducted an analysis where I used binomial logistic regression to analyze x successes in n trials (where n varies between observations) in aggregate (using the R syntax ...
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1answer
31 views

Model/predict the number of malaria-infected cells

Background: In order to determine the severity of a Malaria infection, one takes a sample of red blood cells and determines, through a microscope, the number of cells infect by the malaria parasite. ...
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1answer
312 views

binomial responses in h2o gbm

I am modeling the probability of success in a dataset where I have a both the number of trials and the number of successes (and, obviously, I am modeling $p_i=\frac{total successes}{total trials}$). I ...
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118 views

Calculating a Confidence Interval for a Proportion for a Sample of Different Size

I'm interested in a (preferably analytic) solution or approximation to the following problem: Let $s_1$ be a sample from an unknown distribution of size $N_1$ and with proportion of successes $p_1$. ...
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89 views

Confidence interval of proportion of a proportion

Let's say we have $N$ users. Some of them could be hackers and some not. Only for a random $p_u$ percent (e.g. 1%) of users have we actually investigated manually to know which ones are hackers and ...
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168 views

Confidence intervals and hypothesis tests for binary choice data with repeated measures

I have data with two between-subjects factors (each with two levels; bs1 has levels ‘hi’ and ‘lo’, and bs2 has levels ‘happy’ and ‘sad’) and one within-subjects factor (ws1, with levels ‘good’, ‘...
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1answer
55 views

Summation of combinations up to $r-1$ terms

I am trying to come up with a simplified expression for $$\sum_{k=r}^{n}\binom{n}{k}$$ Choosing $x=y=1$ in Binomial theorem, I have $$2^n = \sum_{k=0}^{n}\binom{n}{k}$$ $$2^n = \sum_{k=0}^{r-1}\binom{...
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1answer
164 views

Appropriate estimation of standard deviation for a sample of proportions

I am working with some bird mortality data across 9 years of surveys and have run up against a problem estimating the standard deviation. Across the 9 years, survival estimates were .47,.60,.36,.58,....
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Detecting outliers in percentages

My dataset looks like below - Total Success Percentage 100 65 65% 50 25 50% 30 20 66.6% 50 40 80% Plot - Each row is ...
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1answer
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sampling order sum from different order size and probabilities

I want to analyze the probable outcomes of an order pipeline for a business. Say we have ten potential orders, each (business) order has a different size (OS), say 1, 20, 3, 4, 5, 6, 6, 8, 8, 9 (mio) ...
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Differences from logistic regression and mixed effects logistic regression - rounding error or conceptual mistake?

I'm a bit confused. To my understanding, the standard logistic regression should be equivalent to a mixed effect logistic regression where the statistical unit is defined as random effect - but I ...
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209 views

Residuals in Negative Binomial Data

I'm tackling the problem of Anomaly Detection in a dataset that's comprised of call counts to a call-centre. The data exhibits daily and weekly seasonality and is known to be over-dispersed. ...
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146 views

Probability of a Blizzard - Poisson vs Binomial vs Bayesian

My goal is to model data I have collected to compute the probability of a severe blizzard occurring in a given set of states (region). Assume the US is broken into 3 regions that categorize the ...
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311 views

Limiting distribution of $\frac{\bar{x}-p}{\frac{pq}{n}}$ from mean of $Bin(1,n)$?

I found some difficulties in here. We know that if $X$ has Binomial distribution with $1$ trial and $p$ success, or what we called $X$~$Bin(1,p)$, we have $\mu=p$ and $\sigma^2=p(1-p)=pq$. From that, ...
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168 views

Sample size formula for multiple regression between binomial variables?

Let's say we have k binomial variables, and a sample size of n observations per variable, where each variable occurs (positive case) at a given frequency/probability f. We would like to check if ...
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279 views

Pattern-mixture models

I am currently looking at pattern-mixture models but I don't seem to understand them and I wonder whether someone could help. I can see the model comes from the factorisation $ f(y,r;\phi, \theta)=...
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72 views

Test of strict difference in independent binomial probabilities

Suppose $X,Y$ are two independent binomial random variables with parameters $n_1,p_1$ and $n_2,p_2$ respectively. Suppose one wanted to test the hypothesis $p_1>p_2$. Conditional on $X+Y=s$, ...
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339 views

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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315 views

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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