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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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Distribution to describe size of population with random exponential growth

Is there a distribution family that describes the size of a population experiencing random exponential growth (either discrete or continuous)? For context, I am trying to computationally model a ...
david's user avatar
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What is the best test to run to compare presence/absence of something between sampling locations?

I have data on the presence/absence of four different pathogens found in edible crabs in 7 locations over 2 seasons. For this study, 30 crabs were collected from each site and for each crab the ...
Kiran Bhandari's user avatar
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Test whether my new method's type I error rate correctly matches chosen alpha

I am testing two different methods for hypothesis testing, bootstrapped likelihood ratio tests, and likelihood ratio tests assuming an asymptotic distribution. I would like to see if the number of ...
A Friendly Fish's user avatar
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Expectation of binomial random variable

Having trouble understanding something I read in a paper recently. Say we have $X \sim \operatorname{Binomial}(N,p).$ The paper states: $$E[X \mid N,p] = Np$$ (so far so good) and $$E[X] = \mu p$$ ...
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Regression strategies for predicting a binomially distributed, count outcome: Poisson, Negative Binomial, and Logistic Models with Offsets

Data Description: I am working with a dataset of 100 hens, represented across four columns: ID: Numbers 1 through 100. Age: Each hen's age. EggCount: Number of eggs laid per hen, with a range from 0 ...
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What is the correct sample size for the purposes of this test?

$X_i$, $i = 1, \ldots, n_X$, are i.i.d. from some distribution; and $Y_j$, $j = 1, \ldots, n_Y$, are i.i.d. from some other distribution. Consider all pairs $(X_i, Y_j)$. The number of pairs is $n=n_X ...
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Rejection region in LRT test

Let's say I have $X_i \sim Bi(1, \theta$) and want to test $H_0: \theta \geq \theta_0$ vs $H_1: \theta < \theta_0$. I've found that $\lambda = \frac{\sup_{\theta \in \Theta_0}L(\theta)}{\sup_{\...
Peter Sampodiras's user avatar
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I would like some insight into what I have been working on here

I work in roofing sales which involves door-knocking at the entry level. Our daily numbers are printed in our GroupMe chat for our branch. I took it upon myself to do some analysis on those numbers. ...
therealchriswoodward's user avatar
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"Important" data points causing problems with nonlinear regression bootstrapping

I am trying to model radar backscatter of a planetary surface. The power which is scattered back to the instrument depends on the angle at which the it observes the surface. The shape of the resulting ...
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Number of successes for correlated Bernoulli variables

The number of successes for a given set of independent Bernoulli random variables is described by the binomial distribution. However, I was wondering what could be said if the Bernoulli variables were ...
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cloglog.sample.size function (Binomial distribution)

I was wondering if cloglog.sample.size function from binom package in R can be used to calculate the sample size for the following model (Binomial dis with cloglog) which can be used for discrete ...
user413503's user avatar
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Distribution of outcomes of multiple binomial distributions

I have a sample of 50 subjects, where every subject completes a task with two possible outcomes (left or right hand use, with 50% probability) 30 times. On an individual level, this leads to a ...
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Probability of leaving with $20

You play a game with a coin. You may place a bet; if Heads is flipped then you receive your bet back plus the same in winnings. If Tails is flipped then you lose your bet. You have 20 dollars and you ...
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How to fit a binomial model with repeated observations per subject

I have a small dataset for 100 participants. The dataset includes repeated 'tests' over a course of a week. A test can have the binary outcome of pass or fail, and the same number of tests are not ...
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Binomial distribution in R is not symmetrical

I expected the code below to produce the same output, but it's not. My thought was based on the the binomial distributon formula for the density function. I use Rstudio. Where is the mistake? $$ P(x) =...
Simone Gheller's user avatar
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Is it true that R(k+1, n+1) < R(k, n)?

Is the following statement correct or not: The probability of having at least k+1 successes in n+1 trials is less than the probability of having at least k successes in n trials. That is, is it true ...
user413516's user avatar
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What is the difference between using logistf and brglm2 when dealing with complete separation in a logistic regression?

I am trying to looking at how the three factors A (5 levels, a-e), B (2 levels, a and b) and C (2 levels, a and b) affect the likelihood of event Y (1 = occured, 0 = did not occur). I initially ran a ...
Insect_biologist's user avatar
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glmer significant and post-hoc test not significant

I ran a glmer model to test the effects of treatment on my response variable ...
GiorgioS's user avatar
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1 answer
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Determining chance level for forced-choice performance validity tests

Psychologists, especially neuropsychologists, use performance validity tests (PVTs) to detect individuals who might intentionally underperform on ability tests, e.g., memory tests, because diagnosed ...
Mark D Worthen PsyD's user avatar
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Binary response vs probability response

Consider these two scenarios: respondents are asked to choose between two options offered to them (the resulting data is binary 0 & 1) respondents are asked to give their probability of choice ...
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Goodness of fit test binomial random variables without "compensation"

Let $N_{1}, N_{2}\in\mathbb{N}^{+}$ and random variables $X_{1}\sim B(N_{1},p_{1}),X_{2}\sim B(N_{2},p_{2})$ with null hypothesis $H_{0}:p_{1}=p_{1,0}, p_{2}=p_{2,0}$. I would like to apply a GoF test ...
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Exam P Sample Problems # 30

The question: A company establishes a fund of 120 from which it wants to pay an amount, C, to any of its 20 employees who achieve a high performance level during the coming year. Each employee has a ...
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Why confidence interval for proportion uses z instead of t score? [duplicate]

The confidence interval (Wald interval) for the parameter $p$ of a binomial distribution is computed from the approximation by a Normal distribution: $$ \ p ~~ \approx ~~ \hat p \pm \frac{\; z_\alpha\ ...
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Multiway McNemar-Type Test?

I need a test that would be similar to McNemar, but has e.g. 3 binary outcomes (0,1). Kappa also comes to mind for something that may be similar like interrator agreement. However, my hypotheses is ...
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Can a GLM Binomial regression on repeated measures be seen as a trustworthy alternative for a Survival Analysis?

I'm working on an actuarial project to estimate monthly probabilities that someone becomes disabled. We have data available in a wide format. For example, the following lines are part of the data: ...
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1 answer
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describing binomial data in likelihood models

Binomial data can be described in various ways. Suppose we flip a fair coin twice and get one head (success). One method to calculate its negative log-likelihood is ...
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binomial data, margin of error, standard error of a sample

Election season is coming soon, and polls frequently have a "margin of error" associated with their results (e.g. there are 2 candidates, and there's a survey, and candidate A is the ...
thanks_in_advance's user avatar
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Binomial mixed model with conditions only ever 'succeeding'

I've been wrestling with getting some models to converge and make sense and think I've identified the problem, but am now looking for a solution (and if you agree with the "problem"). ...
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Analyzing Cumulative Distribution Functions in Sampling Without Replacement vs. With Replacement

Originally asked on MATHEMATICS. I am studying a population of $N$ bits, comprising $K$ ones and $N-K$ zeros. For sampling $n$ bits without replacement, the situation conforms to a hypergeometric ...
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Conditions for Binomial Distribution

It is known that if $X$ is the sum of $n$ independent and identical Bernoulli random variables, $X$ follows a Binomial distribution. How about the reverse, can a sum of dependent and/or non-identical ...
Usermaths88's user avatar
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1 answer
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Next steps - variable can't be a fixed and random effect?

I have been trying to run a binomial GLMM on the proportion of emerged seedlings across locations (categorical variable) and over the monitoring period (continous variable). We obtained and planted ...
TruthSeeker4's user avatar
1 vote
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Am I using the correct test statistic for a binomial glm using the type III Anova function in the package car?

I am trying to look at how the likelihood of event Y is influenced by two factors A (5 levels) and B (2 levels) and my model is as follows: ...
Insect_biologist's user avatar
5 votes
2 answers
166 views

Why do I get a negative chi-squared value in my type III ANOVA output for my binomial GLM?

I am trying to look at how the likelihood of event X occurring is affected by three factors A (5 levels), B (2 levels) and C (3 levels). To do this I have run a binomial glm followed by a type 3 ANOVA ...
Insect_biologist's user avatar
3 votes
2 answers
88 views

Estimate a GLM where the intercept is known

I have some x and y values. The y values have some random error. ...
Dan's user avatar
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GLMM logistic regression with interactions

I have been working on a mixed effects logistic regression model to analyze some data, and I'm seeking some clarification on interpreting the results, particularly when incorporating interaction terms....
Sebastian Rocano's user avatar
4 votes
2 answers
121 views

Confidence interval for the sum of 2 binomially distributed variables

$P_1$ and $P_2$ are uncorrelated, binomially distributed variables with success probabilities $p_1 \neq p_2$. Say I measure: $k_1 = 9$ successes out of $n_1 = 10$ trials for $P_1$ and $k_2 = 1000$ ...
dimitsev's user avatar
1 vote
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Model Fit Measures in a Binomial Logistic Regression

I am very new to regression statistics and have produced four models in the statistical package Jamovi using binomial logistic regression. Looking at model fit measures I am confused as the results ...
Max's user avatar
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1 vote
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Standard deviation of the mean for biased coin with all heads for first $N$ trials

Imagine that we have a biased coin but we only have $N$ trials to determine how much it is biased towards heads (we are resource limited in how many trials we can conduct). Say we assign a value of $0$...
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Predict quality of a product, from production line, by looking at a sample instead of the whole batch

I have a machine that produces cartons. Every batch that is produced is of 3000 cartons. I want to determine what percentage of cartons are GOOD and what percentage are NOT GOOD ( marks on the carton, ...
Aran's user avatar
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0 answers
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Binomial Test for data with normally distributed messurement error

I have a series of measurements and I want to perform a binomial test to see if the chance of exceeding some value $a$ is less or equal to some $p_0$. The measurement has some error which is normally ...
Adrian 's user avatar
3 votes
0 answers
52 views

Forcing GLM with binomial distribution through zero intercept [duplicate]

I have been re-directed to cross-validated after my post here on stack-overflow. I want to force the intercept of a glm model with a binomial link function to be zero, since there are biological ...
Squan Schmaan's user avatar
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27 views

"Bi-bumped" ROC curve meaning?

I am exploring some models for the classification of proteins based on their similarity. Briefly, I am testing the classification with a binomial fit and then analyzing the corresponding ROC curve to ...
Natalia's user avatar
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Confidence interval for binomial distribution [duplicate]

I'm developing a simple application for memorization, for personal use. The user gives responses corresponding to prompts, and each prompt belongs to some category. At the end, we have for each ...
Matt's user avatar
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3 votes
1 answer
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Calculating binomial distribution probability for dependent trials

Context: I am a software developer and recently we've had a bug report saying that one of our login systems are potentially insecure to a brute-force attack. I need to come up with a formula to ...
choket's user avatar
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1 vote
1 answer
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For the binomial distribution, is the proportion of successes distributed the same as the number of successes?

Given a known population proportion and an IID population, the number of successes given n trials should be: $$ X \sim B(n, p) $$ It seems intuitive that the probability of observing a certain ...
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How to test whether the "prevalence ratio" of one marker is higher than that of another

Here is my setup. I have two sets of DNA sequences, one bound by a protein (transcription factor), another not bound by the protein. Let's say I have two candidate motifs, or DNA patterns the protein ...
ffffffyyyy's user avatar
0 votes
1 answer
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Analogue of fisher's exact test for one group?

I understand that Fisher's exact test applies to testing whether the proportion of an outcome in one group, $p_1$, differs from the proportion of the outcome in another group, $p_2$. This could be ...
ffffffyyyy's user avatar
1 vote
1 answer
19 views

What is the distribution of similarites between 2 iterations of a binomial variable?

Suppose I have a binary vector $v$ of dimension $n$ with $np$ entries set to $1$ and $n(1-p)$ entries set to $0$ (where $0 \leq p \leq 1$, and $q:=1-p$). Suppose I then generate a random vector $w$ by ...
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6 votes
1 answer
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Small Sample Sizes and Zero Inflated Count Data in R

I am working to produce a model in R for seed germination count data with lots of zeros (around 50% of the 264 total observations). The purpose is to determine the effect treatments have on plant ...
newspice's user avatar
28 votes
4 answers
3k views

Coin flip game: HH vs HT in a sequence of flips

An interesting thought experiment involving flipping a fair is going around X/Twitter: Flip a fair coin 100 times—it gives a sequence of heads (H) and tails (T). For each HH in the sequence of flips, ...
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