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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32 views

Assessing the meaning of a metric in a binary design

I try to assess the meaning of a software metric lines of code on bug density with the help of statistical methods. I have information on bugs and other needed software measures for several years. ...
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Wilson confidence interval for partially-paired data

I have a data set with paired observations (before and after a specific intervention). There are a lot of metrics in this data set, some of them numeric (of unknown distribution) and some of them ...
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How much confidence to have data is correct based on checking N samples

If I have a dataset of size $N$, and choose $n$ samples, where $k$ of the samples are OK, how confident can I be that the dataset is OK? To make it more concrete, suppose I have a dataset D1 with 5,...
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15 views

Significance Testing for the Difference between Binomials [duplicate]

I have two algorithms, $A_1$ and $A_2$. $A_1$ either accepts or rejects samples from dataset $P$ $A_2$ either accepts or rejects samples from dataset $Q$ Below is a 2x2 contingency table for the ...
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1answer
32 views

Inference in binomial with zero successes and fixed number of trials

Let $X \sim \mathsf{Bin}(n, p)$ where $n$ is known and $p$ is to be inferred from the data. Suppose further that $X = 0,$ so that we had no successes. We can reason in the following way. We want to ...
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2answers
60 views

estimate a binomial parameters (n and p) from a distribution sample

I have found this function def find_np(data): that try to estimate p,n out of a binomial distribution sample: ...
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35 views

Model uncertainty in a logistic regression model - binomial proportion confidence interval

In my line of work I have seen people quantify general model uncertainty, when using a logistic regression model, with an Agresti-Coull confidence interval. I am not convinced that this is correct, ...
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1answer
33 views

How to solve this [closed]

There is this problem from past exam papers that I am trying to solve and I can't any ideas? In a bet between two runners the winner will be the one who wins the other 3 times. If the terrain is wet, ...
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1answer
29 views

Comparing proportions of plants that died (two-way analysis with interest in interaction effect)

I want to compare the proportions of plants in an experiment that had died by the end of the growth period. I am not interested in how long it took for them to die, although I suspect some people ...
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21 views

Variance of binomial estimate mle

I have the estimator: p=1/nt * ∑Xi Not too sure how to go about finding the variance of it
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50 views

What type of data model should I use?

Could someone kindly help me understand how to model my data correctly? Note: I've significantly rewritten my question. I hope that's ok. I am testing the performance of different proteins in bacteria....
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1answer
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Testing for statistical significance of the true positive detection rate between different machine learning models

Background Currently I am working on true positive detection for an image analysis problem. I have 4 methods and would like to test which methods differ from each other. Description of Data For each ...
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2answers
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When calculating the likelihood ratio for 50 heads of 100 coin tosses. What probability should I use for a biased coin?

A quiz asks me to calculate the likelihood ratio for 50 heads out of 100 coin tosses. I understand that a coin can be either fair or not fair and that a fair coin has a probability of 0.5 for heads. ...
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Convolution of Binomial and Poisson Distributions?

I am currently working through the paper Estimation of Probability of Defaults (PD) for Low-Default Portfolios: An Actuarial Approach In Section 2 of this paper, the author provides the following ...
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Why is n not mentioned on the left in binomial probability?

How do I read the left hand side of the equation and why is $n$ not mentioned on the left? The source is here. Referenced from Coursera
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5answers
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Basic Sampling - Provide confidence of estimate

I tried searching the site but nothing came up. I have a simple situation for a business problem - We have a population of 50 million files. We want to review a sample and see whether a file contains ...
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1answer
29 views

Bayesian updating with discrete support

Suppose I have a coin that is either fair ($Pr(H)=0.5$) or biased ($Pr(H)=0.2$). I have a prior probability $Pr(fair)=\tau_{0}$. I observe a sequence of tosses with outcome $X_{1},X_{2},...,X_{n}$, ...
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1answer
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Maximum likelihood estimator for binomial model

The main problem I'm having is that I'm getting $\hat{p}=\frac{\bar{x}}{n}$, not $\frac{x}{n}$. For some reason, many of the derivations of the MLE for the binomial leave out the product and summation ...
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GLM Logit with either Normal or Binomial Distribution

I am fitting several continuous parameters to predict a proportion (0 - 1) outcome. I used a generalized linear model with a link logit and a Normal distribution. I have seen some people recommend ...
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3answers
452 views

Predicting with a GLM

I wanted to check my understanding of predicting with a GLM: A binomial/logistic regression model predicts the binomial parameter = p = P(success). To convert the probability into classes, we have to ...
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Why does redrawing a sample of a binary variable split into two groups generate different distributions according to prop.test()?

I was working on some power calculations and stumbled upon results I don't understand. Say we have a sample of a binary variable a, and the sample probability of success is p. We randomly split the ...
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1answer
37 views

Independence Assumption Simulation?

I'm simulating what happens when you break the assumption of independence when you sample without replacement. The rule of thumb is that you shouldn't sample more that 10% of the population. Kahn ...
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1answer
59 views

Binomial (1/0) response, Factor explanatory variable: why can't GLM estimate effect when one factor level has all 1s in response?

I have a dataset with a binomial response variable (1/0) and a single explanatory categorical variable with 2 levels. For one level, the response is all 1s and no 0s (e.g. ...
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1answer
30 views

When to use offset in binomial glm

I am trying to model the number of successes in data where the number of trials is not fixed. I am trying to fit a binomial generalised mixed effects model, with the number of trials as an 'offset' ...
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17 views

Tight "uniform" tail bounds on binomial distribution

I am interested in upper bounds on the probability $P\left[\frac{X}{n} <p-\delta\right]$ for a binomially distributed random variable $X\sim B(n,p)$, which are both (1) as tight as reasonably ...
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2answers
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Smallest sample size for true proportion estimation (Binomial distribution with 1 found defective unit)

Suppose that we allow only 1 defective unit in the control sample. What is the smallest sample it should be in order to conclude that my true defective proportion of the population is smaller than 0.5%...
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Sorting a bag of biased coins with least flips - is it a well known problem?

I'm working on a practical problem which can be reduced to something like: There is a bag of biased coins of two types with known biases (probability of heads are $p$ and $q$). The approximate ratio ...
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1answer
63 views

Drawing graph of variance using R [closed]

I am a self -learner and try to learn statistics with R ,but i encounter with a problem i could not handle it such that I want to produce a graph of the variance of a binomial distribution with a ...
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2answers
73 views

Find marginal distribution of Y while knowing distribution of X and $Y|X$

Assume that X is uniformly distributed on (0, 1) and that the conditional distribution of Y given $X = x$ is a binomial distribution with parameters $(n, x)$. Then we say that Y has a binomial ...
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1answer
48 views

Hypothesis testing two unfair coins to see if they have 'equal' bias [duplicate]

Consider tossing two unfair coins 100 times: How can I know using the two sets of Heads or Tail results whether the two coins have an equal (or similar) bias with a 95% confidence? I am currently ...
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1answer
31 views

What would be the proper distribution to model the number of particles in a state in canonical ensemble

Suppose my system has $N$ particles, and I want to find a distribution for $n_i$, the number of particles in the $\epsilon_i$ energy state. What I do know is the boltzmann probability, which tells me ...
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1answer
28 views

Confindence Intervals for Ordinal Variable

I count how many days within a month people have executed a certain activity. The maximum is 30 (i.e., the person executed the activity each day), the minimum is 0 (i.e., the person never executed the ...
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1answer
66 views

Machine Learning with Aggregated Frequency Data as Training

I am trying to build a Deep Learning model in which I have the following structure user feature binary_label 1 100 0 2 200 1 3 140 0 ... ... ... 6000000 188 1 But the problem is that when I try ...
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1answer
34 views

Can a Probability Distribution ever "look similar" to a Cumulative Probability Distribution?

Can a Probability Distribution ever "look similar" to a Cumulative Probability Distribution? Suppose in some imaginary town - the height distribution of the residents are as follows: There ...
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1answer
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Does a $100 \times (1-\alpha)$% "exact" binomial CI imply use of the Clopper-Pearson method?

I am working from a protocol to develop table specifications. The existing code which we have adapted for this purpose uses the Clopper-Pearson method to calculate the $100 \times (1-\alpha)$% ...
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2answers
72 views

Difference between multinomial distribution with n trials and categorical distribution performed n times

I want to understand if there is any difference between performing multinomial distribution with 1 trial, 10000 times and performing multinomial distribution with 10000 trials, 1 time. Here is the ...
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19 views

Binomial GLM with Logit Link on Continuous Data given Frequency Weights [duplicate]

I'm wondering what R is doing in the background when given rate/proportion data and frequency weights. The Binomial GLM should only fit {0,1} data but the results still seem fairly accurate. Does it ...
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27 views

Analytic expression for false-negative rate of binomial tests?

I wrote a previous question yesterday which was maybe too long and boring to read. So to try to get an answer, I've boiled down my question to something short and specific which is: Is there an ...
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1answer
85 views

What is the dispersion parameter of binomial distribution?

Binomial distribution is a member of exponential dispersion models, but I can not find the dispersion parameter of it. Could anyone help me find it out? IMO the Binomial distribution only has an ...
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3answers
250 views

How many coin flips are needed to reliably know a coin of weight w is unfair?

I want to find out how many flips I need to flip a coin to reliably know that it is an unfair coin. The issue is that as the coin becomes closer to 50/50, the more false-negatives you will have if you ...
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1answer
97 views

spicy binom_test gives the same answer for alternative greater or less

I'm seeing something very unexpected with the binomial test function in spicy (python). ...
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1answer
41 views

Interpreting binomial test results

I'm relatively new to stats and any help would be appreciated. My experiment has two boxes one baited with food and the other non-baited. I am trying to test whether the probability of the animal ...
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1answer
30 views

How to interpret this binomial distribution result?

From the Binomial distribution, the chance of getting at least 50 heads when flipping a fair coin 100 times is 54% (to 1 d.p.). It seems to imply that that there will be more heads than tails, but ...
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How do I model serial correlation in a binomial model?

I'd like to test for trends in proportions of animals sampled over 12 years at six different beaches so that there is a separate trend test per beach. In the data below 'thisbeach' is the number of ...
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4answers
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How to derive the binomial test?

From what I understand from a pervious question I asked, the p-value for a particular binomial test (specifying a number of flips, and number of heads and tails, and a null-hypothesis to test against) ...
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1answer
32 views

If prop.test is an approximation to binom.test, why don't we use binom.test when computers can do it?

When computing by hand, it makes a lot of sense to approximate the binomial distribution with a normal distribution because otherwise it would be impossible to perform calculations. However, when ...
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9 views

Paired t-test to compare mean of responses to a questionniare. (Binomially distributed data)

I have data from of people filling in a questionnaire where they for each statement give a score on a scale from 0 to 4 where 0 corresponds to them fully disagreeing with the statement and and 4 fully ...
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1answer
51 views

Beta-Binomial mixture vs Beta-Binomial multilevel model?

I first read about the Beta PDF in the context that it was conjugate to the Binomial distribution; a Beta prior with a Binomial likelihood returns a Beta posterior. So this sounds to me like a ...
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24 views

Statistical evaluation of a 'success rate'

A recent TV show concerned with phenomena "that science cannot explain" described the work of a researcher who examined the claim that some people had telepathic powers. I did not note down ...
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1answer
37 views

Transforming the expected value of $Y_i$ in binomial regression

Currently, I'm learning generalized linear regression (GLM). There is something troubling me concerning binomial regression. In this text, in the part about the structure of a GLM, the random ...

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