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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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How do I use Tarone's Z-statistic?

Context In this blog the author suggests using Tarone's Z-statistic to test for overdispersion in a binomial model to determine whether or not it is necessary to use a beta-binomial model instead. In ...
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How to prove or disprove that $T(X_{1},X_{2}) = X_{1} + X_{2}$ is a sufficient statistic

Let $X_{1},X_{2},\ldots,X_{n}$ be random sample from a population whose distribution is given by $X\sim\text{Bernoulli}(\theta)$, $0 < \theta < 1$. a. Show that $T(x) = \displaystyle\sum_{i=1}^{...
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Calculate SD for a given problem specification (see Body) with python

I am new here as you can tell. I have the following problem for which the SD has to be adjusted in order to fit said problem. Problem: Say I have 500 balls which I deliver to a customer and if more ...
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No population? How to answer such question?

Say the givens are: probability of a battery being defective is = 0.40 being not defective = 0.60 STD = 1.5 hours mean = 7.5 hours The question states: if 5 batteries are randomly selected what is ...
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Does the family of binomial distributions conditioned on $X > 0$ belong to the exponential family?

Does the family of distributions where $p(x,\theta)$ is the conditional frequency function of a binomial $\mathcal{B}(n,\theta)$, variable $X$, given that $X > 0$, belong to the exponencial family? ...
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Should filtering be done before or after correction for multiple testing?

I am trying to find allele-specific bias in some biological data. An equivalent problem that doesn't require understanding biology would be trying to determine which coins, if any, in a giant bucket ...
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Sample size for proportions and fisher exact test

I need some clarification. I am doing a chart review. Plan to test significance with fisher exact as its two interventions, one yes/no outcome. Presumed prevalence in the population is 15%, but ...
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Binary models with the regressor that has Bernouli distribution [closed]

I have a binary dependent variable, but my regrerssor also has Bernouli distribution. Will logit still give a consistent estimator in this case? How can I estimate? Is that right? model: y=b1+b2*x b1=...
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Binomial distribution in exponential form

I am trying to find out if I am doing this right: I have started with: $f(y)=\binom{n}{y}(\frac{\mu}{n})^y(1-\frac{\mu}{n})^{n-y}$ This is what I get: Result: $exp[ylog(\frac{\mu}{n-\mu}) - nlog(1+e^...
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zero inflated presence absence binomial GAM in R

I am fitting a binomial GAM using mgcv in R. My data is presence (1)/ absence(0) of dolphin acoustic detections in 10 minute time windows over ~1 year period. However, I have only ~750 presences to ~...
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Expressing Law of Large numbers in terms of binomial probabilities

Suppose I let $p \in (0,1)$. Then for $n \ge 1$ and $0 \le k \le n$ let $${P}(k;n,p) = \dbinom{n}{k} p^k(1-p)^{n-k}$$. How can I express the law of large numbers in terms of the probabilities $P(k;n,...
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How to randomly downsample from matrix [closed]

I'm trying to downsample from a matrix of numbers. Each number is the number of times we saw a particular event. By downsample I mean I want to pseudo-randomly select values from each row so they ...
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Is my use of the binomial distribution right here?

I have data from two separate experiments, which I'll call "control" and "experiment". The outcome from each trial is a "yes" or a "no". In the control group, 87% of participants got a "yes". I am ...
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Can (log-)likelihood be used to compare a binomial model to its beta-binomial equivalent?

In this article the author talks about fitting beta-binomial models to data when the there data is over-dispersed relative to the assumptions of a model with binomial errors. Near the end they present ...
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How many tests should I perform to establish A% confidence in a p (unknown) probability of success?

I have a random variable X that follows the binomial distribution. I can only perform n observations on this random variable. I do not know the probability of success, p. Please advise me if the ...
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Estimate value with binomial distribution [closed]

We have some compound A diluted in a solution. In 200 trials, we find that when we mix $1$ $\mathrm{mm}^3$ our solution of A with some amount of some compound B, we get a reaction 185 times. How can I ...
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Interpretation of the region of rejection in hypothesis testing in binomial distribution

The pharmacy company Life Co. has developed a new drug against insomnia. To check the effectiveness, this drug was tested with n = 10 patients. At present, the standard medication can cure 30% of the ...
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Statistics for a probability parameter

I am measuring how humans perform a perceptual test. The graph shows the proportion of correct responses as a function of an independent variable x for one person. The model includes a lapse ...
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Can I remove random effect from my model?

I have some data which I am getting a singular fit error and I would like to work out the reason so I can decide whether I can remove the random factor from the model. I have 835 data points with a ...
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Maximum likelihood estimator of $n$ when $X \sim \mathrm{Bin}(n,p)$

Given a random variable $X\sim Bin(n,p)$, where $p$ is known $p\in (0,1)$ , $n$ is an unknown positive integer and $x\in\{0,1,2,....n\}$, what is the maximum likelihood estimator of $n$? I ...
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Minimum variance of logit(p)

Let's say that we have $X_i \in Bin(n,p), i=1,...,n, iid$. How can we find the minimum possible variance of an unbiased estimator of $logit(p) = \log(\frac{p}{1-p})$ ? My thought is the following, ...
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Yes/no GZLMM zero inflated

I have got a variable which I want to analyse using a GZLMM with binomial distribution as the variable is coded as yes/no(1/0). However, there are a lot of zeros and not many 1's.I was hoping to ...
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critical region of a binomial population

I have the following homework problem: The number of successes in $n$ trials is to be used to test the null hypothesis that the parameter $\theta$ of a binomial population equals 0.5 against the ...
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1answer
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Why does differentiating the normalization term of a Binomial Distribution yield the expected value? [closed]

In Bishop's book Pattern Recognition and Machine Learning, problem 2.4 aims to derive the expected value of the binomial distribution $m \sim Bin(N, \mu) = {N \choose m} \mu^m (1 - \mu)^{N-m}$ by ...
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Does it make sense to scale categorical variables in glmer when they have three levels?

I am trying to fit a generalised mixed effects model, but I am having convergence problems. The model I want to fit is ...
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1answer
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Bayesian inference on binarized Poisson distribution

I have a variable that is Poisson distributed. Let's say I have a number of boxes each with a number of balls inside according to a Poisson distribution, with $\lambda=0.4$, (the average number of ...
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Standard error of estimation - Statistics

I have 2 sets of data X and Y for results of an exam. X - [some random exam result for exam x] - Number of data for x is 110 Y - [some random exam result for exam y] - Number of data for y is 130 ...
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Binomial logistic regression with multiple Likert-scale (ordinal) predictors

My colleague wants to perform binomial logistic regression with data that include: binomial (T/F) response variable 35 different Likert-scale (1-5) predictor variables to choose between. N = 300 ...
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Calculating the variance and expected value of a multiple Coin Toss with Reward

I was wondering if you flipped 4 coin tosses, and you get 0.25 dollars for each coin that lands on tails and 0 dollars if it lands on head. How, would you calculate the variance and expected value.
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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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Warning message when using a binomial distribution in glmer() models in R

I asked a similar question in the R forum but realized that isn't the optimal place to post. I'm working with a dataset looking like this: ...
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Finding the mean and variance of an infinite server queue

I am presented with the following homework problem: Let $X(t)$, $t > 0$, be the infinite server queue and suppose that initially there are $x$ customers present. Compute the mean and variance of $...
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Sign test for multivariate time series models

I'm trying to model 98 covariate time series (using CARBayesST in R). I want to make sure that the residuals look nice, so a sign change test is of interest (since I saw that some series had a ...
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1answer
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Power analysis for binomial regression (success/failure)

I've collect 161 people for a study which the original power analysis was based on correlations, but now I've realised binomial regression would be better. I can find a lot of articles on comparing ...
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Discrete uniform vs binomial distribution

Situation: a box contains N balls numbered $1,2...,N$. $N$ unknown. $n$ balls drawn using SRS with replacement and number recorded. A random variable $X$ is defined as the number recorded on $ith$ ...
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regression analysis in questionnaire [closed]

I am performing both descriptive analysis and a logistic regression on a questionnaire`s data that I have sampled regarding Fibromyalgia. Data consists of symptoms that are dependent dichotomous ...
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two binomial distributions of widely different size - confidence intervals, p-values or z-scores?

I was hoping for a bit of help. I have two very different sized samples of binomial distribution, and I want to figure out if they are significantly different. A previous question posted on here has ...
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Required sample size to reach adequate power of a test

We got two types of treatment (type 1 and type 2). In our opinion, type 2 treatment has a higher performance and we would like to show this with research. We assume that type 1 treatment has a maximum ...
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How will p-values behave when fitting normal/poisson to binomial?

I know p-values behave uniformly. Now as p(np) is fixed and n goes to infinity, binomial converges to normal(poisson). Now suppose I take random binomial samplings and fir normal(poisson) to it, for ...
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Estimate sample size for cumulative distribution function

I'm measuring two conversion rates. I'm interested if the difference between them is at least some percentage unit in one direction. I'm assuming both sample proportions are normally distributed over ...
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2answers
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Confusion with simple Binomial Distribution example

I'm following the paper available here. The Binomial distribution is used to calculate the probability of obtaining 26 babies of the same sex from a total of 44 births. If the probability of giving ...
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Inconsist results in binom.test() in R?

I have a question regarding binom.test() in R (3.3.3 on Windows 10): I have a null hypothesis that the p(success)=0.0033 and I want to know whether I can reject this null hypothesis at a signficance ...
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How to compare between multiple factors in GLM

I have read many books and papers comparing GLMS with just a couple of factors with 2 levels, however I am trying to compare whether the presence of parasites differs by month over a 12 month period. ...
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1answer
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How do I find bias and variance of estimators of a binomial distribution?

A product-lot arrives in two containers with respectively 300 and 700 units in each container. We examine 30 units in the first container and find that 𝑋1 of them is defective. We check 70 units in ...
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1answer
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Favorite sequence in 10 flip tosses

I have the following question. Somebody likes to flip coins. In particular, this person is delighted to get a sequence HTTH. Assuming the person flipped coins 10 times, what is the probability that ...
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Centering / standardizing leads to very different results for GLM (logistic, poisson, negative binomial distribution)

I have a dataset with count data and around 1 million observations. My regressions contain around 40 variables (binary and continuous) and 10 thousand fixed effects. I analyze this dataset with linear,...
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Number of succesive fails in a Bernoulli trial [duplicate]

So, I have a standard Bernoulli trial with $N$ independent trials, each having probability of success $p_s$ and probability of failing $p_e=1-p_s$. However, I am interested in finding out two things: ...
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Testing for non-zero values above and below the diagonal of a matrix

I have a $n\times n$ contingency matrix comparing count data (classification) of two procedures. I want to test for non-zero values above and below the diagonal (different classifications in both ...
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When to use variance stabilizing method?

Let's suppose we want to estimate $p$ from $m$ independant realisations of $X\sim Bin(n,p)$: $x_1,x_2,\dots,x_m$, with respective size $n_i$ $i$ in $\{1,\dots,m\}$. Let $p_i$ be $p_i:=x_i/n_i$. To ...
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1answer
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How to figure out whether a coin is “weighted” with some number of flips

Suppose there's a weighted coin. That coin either lands on heads every 1/10 times it is tossed, or it never lands on heads at all. I don't know whether that coin is the type of coin that lands on ...