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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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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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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 ...
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Relation between binomial and negative binomial

I was reading on negative binomial from a Statistics textbook and came across this portion on probability relation between binomial and negative binomial. $Y$ refers to the number of trials required ...
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How to reconcile the frequentist method with assessing the fairness of a coin?

Imagine I have a factory for assessing the fairness of coins. I have no assumptions on the coins; i.e, a given coin has an equal probability of exhibiting any form of "bias". For example. the ...
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Calculate 5th percentile of a rate difference curve generated from a joint probability mass function

I have these curves below: These curves were generated using a library called discreteRV. ...
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What efficient methods are there to assert that a population has a uniform distribution?

I stumbled upon this article on confidence intervals. The concept as a whole made sense but seemed strange to me. I concluded that given a fixed method of randomly sampling the population, a fixed ...
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Using binomial distribution in arrivals [closed]

I have the followig question: Suppose the number of customers arriving is recorded over a 7 days period. Assume that number of customers arriving in a given day are independent. Let Y the number of ...
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Nested ANOVA (half sibling design) using binomial data?

Short question: I was wondering what kind of nested ANOVA-style analyses are available for binomial data? I would like to specifically compare the variances between Level A groups, but also between ...
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CDF of the sum of two independent binomials

I'm wondering if I have cheated here? A sporting team, 41 games, 45% chance of winning a home game, 30% chance of winning away game. 18 home games, 23 away games. Assume that each game is ...
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For binomial success / fail data, how to calculate if the time since last success is out of the normal range

Struggling to figure this out. I have data sets that are essentially ObjectId, Date, Pass/Fail (1/0) The data is normally daily. What I want to figure out is IF the number of days since the last ...
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Standard error of individual groups in a multinomial distribution

Let's say I have a sample of data from a multinomial distribution with 10 categories. I want to determine the error in my estimate of the % of observations that fall into each of the categories. ...
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What is actually being modeled in binomial logistic regression?

One thing I've been struggling with for a while is this: When the binomial logistic regression model includes different number of trials across the observations, what are we estimating at the end of ...
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Binomial distribution intituition for N

I am unable to convince myself intuitively as to why the variance of a binomial distribution increases with increase in n (number of trials). In general, I expect that as n increases, the distribution ...
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Modelling binomial outcome in repeated measures design using glmer

I have a complex dataset for a repeated measures design. Each participant (N=53) saw a total of 72 images that varied according to three different properties (2 categorical and 1 ordinal independent ...
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R: generalised additive model on proportional data

Introduction I am analysing temporal population data on the amphipod Orchestia gammarellus. At several moments each year, all animals were collected from a small spot, and several life history traits ...
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Sample size for the normal approximation of the Binomial distribution

I am reading about the familiar hypothesis test for proportions, using the normal approximation for large sample sizes. Some people say (write) that the condition for using the approximation is np>5 ...
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Binomial GLM: is it valid to use proportion for the endogenous variable, without weighting based on number of trials?

I am struggling with something that seems like it should be relatively straight forward, but my searches thus far have not yielded results. Earlier guidance on the site suggests that when using a ...
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How many neurons are actually dropped when using dropout?

I understand that when using dropout, a single neuron can be described using Bernoulli random variable and for a set of neurons it can be described as Binomial random variable When using Dropout, we ...
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Is it possible to fit a binomial cumulative distribution with only three data points in R?

I have three data points (0,0), (30,0.1538), (60,0.4914). Is it possible to fit a binomial cumulative distribution function only using these three points in R? If not, what sort of extra information ...
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maximum likelihood of binomial distribution over number of outcomes (k) with known probability (p)

I've tried to find the answer to this question, but have been unsuccessful I'm curious if there is a way to use a ML estimator to find the optimal number of outcomes ($k$) to maximize the binomial ...
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incorporating temporal autocorrelation into GLMM

I am examining the relationship between presence at a site over time, and I am interested in determining if there is a decline in presence as an individual gets closer to their final departure. Due ...
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Modelling an response that is an intersection

I am trying to model a variable which is the result of an intersection of words. For example: a = ["apple", "orange", "pear"] b = ["apple", "orange", "carrot"] The number of intersecting words ...
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Predict a disease with a compositionnal count data

I am trying to predict a disease (binomial response TRUE or FALSE) with count data (16S microbiom count) and I got one random effect (person's mother). Actually, im working on count's proportion ...
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Binomial distribution for randomly drawn probabilities

Setting Probability theory can be a weird place sometimes. Here I was, confident in my insane math skills, trying to solve the following problem: Let $N, \alpha$ and $\beta$ be given. ...
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Formula for Power of Upper Tail Sign Test

Given Consider the upper tail $H_0: \theta \leq 0 \,\,\, \text{vs} \,\,\, H_A: \theta > 0$ sign test with the test statistic $B = \sum_{i=1}^n{\psi_i}$ where $\psi_i = \mathbb{I}(Z_i > \theta)$...
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Checking my combinatorics

I am modelling a flash memory system where 0.3 requests are writes (and so take 100 cycles to complete) and 0.7 are read-only (and so take 50). The system can handle 4 requests at once (the ...
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Dealing with complete separation in Generalized Additive Models

Related to "How to deal with perfect separation in logistic regression?": I am modelling survival using a binomial mixed model (gamm from ...
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Why is the conditional distribution from a multinomial a binomial with these parameters?

Say we have a multinational distribution , $$Y=(Y_{1},Y_{2},Y_{3},Y_{4},Y_{5}) \sim multi(n,\frac{1}{2},\frac{\theta}{4},\frac{1-\theta}{4},\frac{1-\theta}{4},\frac{\theta}{4})$$ with observed $X=(...
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Properties of Nonparametric Test Statistics $B$

Given Consider the upper tail $H_0: \theta \leq 0 \,\,\, \text{vs} \,\,\, H_a: \theta > 0$ sign test with the test statistic $B = \sum_{i=1}^n{\psi_i}$ where $\psi_i = \mathbb{I}(Z_i > \theta)$...
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ANOVA and binomial distributions

I am really struggling with this question: Given the assumptions for t-tests and ANOVAs, should data generated by a binomial process be analyzed with them? Obviously, no. However we ran several ...
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Dealing with a binomial outcome, is it correct to apply Mixed Logistic Regression in order to analyze plant's seed viability?

I've been reading several questions asked in this website but I couldn't quite find the answer that I'm looking for. It seems that my experimental design it's not that typical. It goes like this: I ...
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binomial pairs probability

A group of four people is said to be “interesting", if there are at most five pairs who are friends. Assume that each pair of people are friends, independent of every other pair, with probability 1/2 ....
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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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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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Residual Deviance and degrees of freedom - Negative Binomial Distribution

I am trying to model count data using python's statsmodels module (Beer's sold at a football stadium as function of visitors, "tilskuer", and weather data). ...
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Expected value of $e^{sP}$ where s is a complex number and P is a Poisson rv

For each positive integer $N$, let $ B_N$ be a binomial $(N,1/3)$ random variable and $P$ be a Poisson(5) random variable. I am trying to understand the statistics of $B_P$. Could someone please hint ...
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Probability mass function of n dices thrown twice [duplicate]

You roll n dices independently from the other rolls. Than you roll again the dices that show a number other than 4. X = number of 4s. a. What is the kind of the distribution of X? What are the ...
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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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Calculating the true error comprised of two probability distributions

Let $X$ = {0,1,2,3,4} and $Y$ = {0,1}. A probability distribution $D$ defined on $X\times Y$ such that $D_x$ = Binomial(4, 0.5) and $D_{y\mid x}$ = Bernoulli(0.5). Given the predictor: $h(x)$ = $0$ ...
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Symmetrical nature of binomial distribution [closed]

If $X$ is a $binomial(n,p)$ random variable, and $P(X<15)<0.5$ Find $n$. Less than $30$ More than $30$ Equal to $30$ None of the above. I know that binomial distribution is symmetric when ...
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Binomial Distribution - further tests

I have a fairly large sample size of tenants and their average length of stay. When I try to put the data into a histogram, I don't seem to get a normally distributed data set because there is a large ...
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What is the correct terminology for repeating groups of coin flips multiple times in a simulation?

I previously posted a question that is causing a lot of confusion because my terminology is incorrect. I decided to post this question to ensure I am starting my problem with the correct terminology. ...
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How does scipy calculate the binomial CDF so fast?

I ran scipy.stats.binom.cdf(500006, 1000000, 0.5) and it took less than a milisecond. This is crazy as binomial CDF involves summing up a bunch of binomial coefficients. What approximation algorithm ...
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Comparing generated observation from binomial distribution

I am solving this question and I am stuck after few steps, Please help in understanding and proceeding : (a) Generate 100 observation from binomial distribution with your choice of n (>1) and p (...
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Sum of Bernoulli random variables with Gaussian noise

This relates to a question asked recently where (one of the edits of) the question asked what happens when a sum of Bernoulli random variables has some form of noise on the probability parameter. ...
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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 <...