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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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Question related to equation in paper involving bernoulli process

So I'm reading a paper about optimization of design of structures. The author defines H(p) as the function that returns the cost of failure given decision variable <...
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1answer
87 views

What is the distribution of the difference between two random numbers?

I have a big bag of balls, each one marked with a number between 0 and $n$. The same number may appear on more than one ball. We can assume that the numbers on the balls follow a binomial distribution....
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33 views

specific equation for modified wilson confidence interval

I recently read the Brown, Cai, Dasgupta paper on interval estimation for a binomial proportion where they propose the modified wilson method as a better alternative to the standard wald interval. I ...
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15 views

Confidence Interval for accuracy - Binomial?

Imagine we fit the same data mining model on 100 different validation datasets and accuracy is always exactly 95%. If we now use the Binomial proportion confidence interval we would have a standard ...
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1answer
26 views

A priori contrast for binomial GLM

after much reading I decided to write because I cannot find a solution to my question. I already did a priori contrasts before for a continuous variable with normal distribution. Now I have another ...
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2answers
39 views

How is the standard deviation in this coin tossing experiment calculated?

I'm reading Hypothesis Testing: The Basics, there is such an experiment: So, we have a coin. Our null hypothesis is that this coin is fair. We flip it 100 times and it comes up heads 51 times. Do ...
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1answer
14 views

Standard deviation of sum of samples from Bernoulli/Binomial

This should be simple I hope. In lecture notes from a physics course, the professor writes: $\text{Prob(success)}=\dfrac{k}{N}$. So query $q$ times, see some number $\mathcal{l}$ successes and ...
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13 views

How do we perform residual analysis on binomial model with small counts?

I know that both Pearson and Deviance residuals tend to be approximately normal for Poisson and Binomial model with large counts when standardized, so we can exploit that to perform the residual ...
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11 views

Type I and II errors accounted for by one equation?

On this website: https://clincalc.com/stats/samplesize.aspx both type I and II errors are accounted for by the one equation. Surely, because a type I error involves too much positive variance and a ...
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17 views

Validate Binomial distribution exercise with pullets and cockerels

The exercise is as follows: The owner of chicken farm knows, that the event of hatching out a cockerel is three time more frequent than a pullet. One should count the probability, that from five ...
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0answers
9 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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1answer
40 views

Two approaches for finding a MLE in a binomial setting

I'm learning towards an exam in mathematical statistics and I came across the following question. I was wondering if the second approach of solving the question is legitimate. If both are correct, is ...
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17 views

Test for average of independent, non-Identical binomial distributions

I have a box with $m$ coins, each with a probability $p_i$ for $1\leq i \leq m$ of flipping heads. As an experiment, I flip each coin $n_i$ times, recording the results. What is a statistical test I ...
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52 views

Assess statistical significance with before & after binomial data from few participants

For the quantitative analysis of a pedagogical approach, I applied a series of (equivalent) tests prior and after lessons. I want to evaluate the reading (proper identification of sounds from written ...
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1answer
166 views

Unbiased estimator of binomial PMF

Is there an unbiased estimator of PMF of a random variable $Y=\sum_{i=1}^{n} X_n $ where $X_i$ are independent Bernoulli trials with probability $p$, that is, the estimator of: \begin{equation}\tag{1} ...
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33 views

Should I use a binomial glm, beta regression, uniform continuous distribution or nls with logistic regression for probabilities?

I made an individual based model in which there is a population of three types of individuals (lizards) that disperse randomly until they encounter another individual that has a beneficial effect on ...
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22 views

Simple arithmetic approximations to categorical analyses

Suppose I have a two by two table: $$ \begin{array}{c|ccc} & Y & \neg Y & \\ \hline X & a & b& &\\ \neg X & c & d& &\\ \end{array} $$ and I am interested ...
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1answer
127 views

Binomial CDF - Wikipedia vs Reality

The Binomial distribution article on Wikipedia defines the binomial CDF as $F_{Bin(n,p)}(k) = I_{1-p}(n-k, k+1)$, where $I$ is the regularized incomplete beta function. There is a proof for the ...
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3answers
140 views

Deriving likelihood function of binomial distribution, confusion over exponents

This question focuses on a specific aspect of this one: How to derive the likelihood function for binomial distribution for parameter estimation? In my own derivation, I start with: $$f(x\mid p) = ...
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1answer
52 views

Compare species count data between sites

I'm comparing species counts between areas. My data is very similar to the below. ...
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1answer
35 views

Reporting zero inflated negative binomial regression in APA style

I have results to a Zero-inflated negative binomial regression. What is the general "formula" to reporting the significance of a coefficient in the APA style. Is it similar to the "formula" for ...
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1answer
24 views

Probability distribution for draws with conditional replacement? (or how many matches does it take to beat Yugi The Destiny?)

While trying to figure out an old video game, I seem to have stumbled upon a problem that's halfway between a binomial distribution problem and a hyper-geometric distribution problem. With the hopes ...
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1answer
39 views

Binary coin toss statistics

I'm really new to statistics and I'm working on a project where I'm basically trying to rig a coin toss. I have three groups and $n = 50$ tosses for each group: Control (24/50 success) vs treatment 1 ...
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2answers
35 views

How was p-value calculated in this Wikipedia example of a Binomial test

Consider the following example from This binomial test wikipedia article: Suppose we have a board game that depends on the roll of one die and attaches special importance to rolling a 6. In a ...
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1answer
25 views

Expectation of a discrete random variable that is case-defined from other discrete random variables

Background The question arises from the following real-life situation: I buy a newspaper at 3 dollars and sell it at 6 dollars. I know the demand for news paper is a binomial random variable with $n=...
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30 views

When calculating sum of observation in Bayes Theorem, why do we remove one outcome?

relatively quick question regarding this course question: Hearing about your brilliant success in working with M&Ms, Mars Inc. transfers you over to the Skittles department. They recently have ...
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22 views

Hypothesis Testing For Binomial Distribution

I have come across the following problem which confused me quite a lot and would be helpful to get your comments: Problem Suppose we are testing a newly programmed random number generator. We use ...
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1answer
80 views

Binomial distribution as likelihood in Bayesian modeling. When (not) to use it?

I am currently trying to figure out some strangeness about using the Binomial distribution in Bayesian modeling to define the likelihood. To make an example assume I have two conditions, and in each ...
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34 views

Statistics of a function of a binomial variable

I'm struggling with a statistics problem. Sadly, I'm not a statistician. Maybe someone here who knows more than me (a low bar) can offer some pointers. I have a population that gets divided, ...
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22 views

Testing the goodness-of-fit for the binomial distribution

As specified in the title, I'm trying to understand how to test the goodness-of-fit for the binomial distribution; to this aim, I followed what suggested in this link. Particularly, I'm investigating ...
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1answer
27 views

Moment generating function of binomial distribution

I have a test statistics $S(\theta_0) = $ number of $[X_i>0] $ that follows a binomail distribution iwth $p=\frac{1}{2}$. With the standardized test statitics is $S=\frac{S(\theta_0)-(\frac{n}{2})}{...
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20 views

when an exact binomial confidence interval should be used?

Is exact binomial confidence interval only appropriate for extremely rare events or extremely frequent events? If so, what are the rule of thumb for the definitions of extremely rare (<0.01?) And ...
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1answer
27 views

How to realize binomial test in R using data? [closed]

I should do test these data using binomial test (2 first tasks). I have no idea how to do this! I will appreciate any help or mind-joggers!
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43 views

Binomial distribution, hypotheses testing

Suppose the following instance of the hypotheses testing: suppose that the true state of the coin is that it is either exactly fair, or that it shows heads with probability $0.51$, and there are no ...
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1answer
18 views

Confidence interval for the square of binomial probability

I have a binomial distribution where the estimate for p is 0.03 out of 1000 sample trials. Using the normal approximation and Chi-square distribution for the square of normal distribution, how can I ...
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16 views

Estimate probability from sample frequency in a binomial distribution [duplicate]

If I get $s$ successes out of $n$ trials in a binomial distribution, what is the probability $p$ of getting a success in each individual trial? Presumably $p = s/n$, but what if $s = 0$ or $s = n$? ...
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3answers
57 views

Square of Binomial is Chi-Square?

my statistics professor said in passing that if you square the binomial test statistic, you can derive the chi-square statistic. I tried working out the proof, but I can't seem to reduce the chi-...
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1answer
25 views

Binomial and Normal distribution X~N(18,5^2) [closed]

I'm stuck with a problem related to binomial and Normal distribution. Suppose the amount of time a laptop battery holds its charge is: $X \sim N(18,5^2)$ Suppose there are 40 students and there is ...
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141 views

Probability of sum of sequences of integers

Let K be a positive integer.Suppose that the integers 1,2,3,...,3k+1are written down in random order.What is the probability that at no time during this process, the sum of the integers that have been ...
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3answers
125 views

Fairness of 6 sided die NOT using Chi Square Test

So I was reading a lot of online articles using the chi-square test to determine the fairness of a die. Correct me if I am wrong, but isn't the drawbacks of using a goodness of fit test is that you ...
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1answer
40 views

Mixed-effect logistic regression in R, Error: no random effect specified

In a study per-field disease incidences were collected by sampling 35 plants in each field and counting proportion of infected ones (# of infected/total sampled). In result, each sampling location ...
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1answer
28 views

Test for significant differences in two groups of binomial data

In a study per-field disease incidences were collected by sampling 35 plants in each field and counting proportion of infected ones (# of infected/total sampled). In result, each sampling location ...
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0answers
35 views

Zero inflated binomial for excessive zeros

"What are some tricks for dealing with a zero inflated response variable when tackling a machine learning regression problem?" Answer : "One of the easiest and most intuitive methods is to run a ...
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0answers
34 views

Determining sample size for a binomial distribution for a given confidence interval when the probability is close to 0 or 1

I've found formulas for determining sample size for when the probability isn't close to 0 to 1. However for the case when it is close to 0 or 1 I'm unable to find any formulas.
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2answers
66 views

What does it mean to model data as binomial?

On Wikipedia it says [T]he binomial distribution with parameters $n$ and $p$ is the discrete probability distribution of the number of successes in a sequence of n independent experiments, ...
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2answers
109 views

Bayesian inference - iterative updating with Bernoulli distribution (solved)

Suppose I pull samples from a Bernoulli distribution $\mathcal{B}(\theta)$ I don't know the value of $\theta$, but in my case I know that $\theta$ can only have 11 discrete values, $\theta \in \{0....
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0answers
22 views

Double exponential family

The double exponential family is defined by $\bar{f}(y;\mu,\theta) =c(\mu,\theta)\theta^\frac{1}{2}e_Y(y;\mu)^\theta e_Y(y;y)^{1-\theta} $ For the double Poisson distribution, several papers state ...
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2answers
762 views

Is there any better alternative to Linear Probability Model?

I read here, here, here, and elsewhere that linear probability model (LPM) might be used to get risk differences when the outcome variable is binomial. LPM has some advantages such as ease of ...
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28 views

Tukey to check level differences after binomial logistic regression with glm()

I wonder whether the method proposed at this link is correct for my case: Comparing levels of factors after a GLM in R I want to use a binomial logistic regression to assess differences between the 3 ...
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1answer
54 views

Reporting binomial logistic regression

I want to report the results of a binomial logistic regression where I want to assess difference between the 3 levels of a factor (called System) on the dependent variable (called Response) taking two ...