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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Standard Error of the ratio of Binomial Distributions

What's the right way to compute the Standard Error of the Mean of the ratio of two random variables that follow a binomial distribution? I asked a similar question here using Weibull distributions ...
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Confidence interval for function of the parameter - small sample size

I am trying to come up with a solution for this problem. Consider the following set of random variables: \begin{align*} X_{11},...,X_{1n_{1}}\quad &\text{i.i.d. Bernoulli(1-$e^{-\lambda_{1}}$)}\\ ...
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analytically finding the dispersion of beta distribution in multilevel bayesian model

I want to create a multilevel bayesian model of the format depicted in the in figure below. I am examining # of conversions (out of total number of exposures) in multiple subgroups. The conversion ...
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Distribution of p-values - Binomial test

I heard that under the null hypothesis the p-value distribution should be uniform. However, simulations of binomial test in MATLAB return very different-from-uniform distributions with mean larger ...
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28 views

How to plot the cumulative distribution function of std normal dist/smooth curve, step functions [closed]

Look for “pnorm” and “pbinom” in help. Use these commands to plot the cumulative distribution function of the standard normal distribution (of parameters 0,1) and of binomial distributions of ...
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How to process Binomial-Binomial data on SPSS for hypothesis testing?

There are 2 groups of 100 pregnant women: the first are malnourished and the second are well-nourished. A COHORT research is being done on them to determine if malnutrition is a risk factor for low ...
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27 views

Variance of binomial vs. multinomial distribution in cross-validation

Suppose we have a dataset with $N=100$ observations. We do $K$-fold cross-validation with $K=10$ and $K=100$. In the first case, the classification decisions are sampled (can I say it like this?) ...
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Fitting a GLM for binomial data in R

I am an R beginner and out of my depth! I am trying to build a model to analyse data regarding fertility in 2 populations of different levels of sexual selection(M and P), both of which have undergone ...
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34 views

Hypothesis test of 2 proportions, with $np < 5$

We are frequently conducting one-tailed hypothesis tests for 2 proportions ($H_0: p_1-p_2=0;\, H_1: p_1-p_2 > 0$). However, $p_2$ is relatively small in terms of $n, x$ and in some cases we find ...
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2answers
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Is chi-squared valid in this scenario?

I'd like to know whether I am misusing Pearson's chi-squared test. And if so, what should I be doing instead. I've a game-playing program, a "bot", for a zero-sum two-player game. To improve it, many ...
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1answer
35 views

Testing whether data follows a binomial distribution vs. multinomial [closed]

I want to test whether my data follow a binomial distribution or multinomial. So the null hypothesis is H0: X follows binomial, Ha: X follows multinomial. I have hard time applying chi-square goodness ...
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1answer
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Comparing survival times in small samples for two groups

I am working on a dataset of big cats. 18 cats have a particular antigen and the rest (58) do not. We have contact times for when blood samples were taken - so when the cats were identified as having ...
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1answer
33 views

Censored Binomial model - log likelihood

I have a dataset with multiple samples of batches of observations (e.g. one batch of 20 obs., one batch of 50 obs,, etc.). There is a probability that the batches have contaminated observations, with ...
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1answer
34 views

What measures the y-axis in stat_smooth, ggplot2 in R? [closed]

I am fairly new with logistic regression. I have a binary response. And did this plot. The binary response is: Y = 0: The student fails Y = 1: The student succeed ...
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1answer
109 views

Problem with pbinom in R (and binom.dist() in Excel)

I understand that the R-function pbinom(0, 100, 0.5, lower.tail=FALSE) returns the probability of getting 0 or more heads in 100 trials. R gives the correct ...
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Beta-binomial logistic regression model for binomial data with small samples

I have fitted a nonlinear beta-binomial logistic regression model on data y_i: y_i ~ beta-binom(n_i,mu_i,\Phi) where mu_i = exp(\eta_i)/(1+exp(\eta_i)) , and \eta_i=\beta_0+\beta_1/(1+exp(\beta_2x_i ...
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Difference between binomial, binomial() and 'binomial' [migrated]

What is the difference between binomial, binomial() and 'binomial' when using glm. They are not identical, as can be see by following code: ...
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Bivariate distribution: beta and binomial

Consider a pair of RVs $X$ and $Y$, with the following conditional distributions: $$X | Y=y \sim Binom(L, y)$$ $$Y | X=x \sim Beta(\alpha + x, \nu)$$ where $L$, $\alpha$, and $\nu$; are all ...
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1answer
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Post-hoc test after a GLM with binary data

I have run various logistic regressions (GLM) from the binomial family and they have produced some very interesting results. I would now like to run post-hoc tests to find out which levels of the ...
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19 views

Probability of students in a test

So I know this may seem like a simple question, but i'm a student and the difference seems trivial but confusing to me. So basically you have 2 types of students in a class, guessers and swaters. ...
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25 views

Generalised Likelihood Models

Why would you use a re-scaled binomial distribution rather than just the standard binomial distribution as the distributional assumption in a GLM?
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rbinom() produces NA values. What's wrong?

I have to generate RV from a binomial distribution with R . I have a vector for $n$ and a vector for $p$ and for each component I have to generate a random variable. My idea was the following for ...
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Generation of random variables [migrated]

I have a problem about the generation of random variables with R . I have to generate random variables $X_{ij}$ (i=1,...,25, j=1,...,5 ) knowing that each X_ij follows a binomial distribution ...
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2answers
29 views

Maximum likelihood estimation of p in a Binomial sample

Assuming I need to find the ML estimator for p, p being the chance of success in a Binomial experiment $Bin(N,p)$, I would expect my density function to be: $$ f(y) = {{N}\choose{y}} p^y(1-p)^{N-y} ...
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Estimate probability mass function from observed samples?

This question is related to but is distinct from Estimation of probability mass function using finite samples. As in the related question, suppose we have a discrete random variable $X$ with known ...
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binomial confidence including run to run variation for overdispersion

I'm trying to determine the model to correct a confidence interval (binomial proportion for example) but to also include overdispersion affects that arise from a Run-to-Run variation. Example, case ...
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173 views

Probability distribution for a proportion based on (continuous) quantities

I have a problem related with probability distributions and parameter estimation, which comes from a real case. I would be very grateful if you could help me. Let us suppose that we have a continuous ...
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Binomial regression does not give coefficients for all IVs [duplicate]

I have a dataset with the dependent variable presence / absence (0 and 1) for a certain species. I have three categorised IV's (2 IV's with 3 categories and 1 with 2 categories). To test the response ...
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42 views

How to calculate the absolute central moment of a Binomial distribution?

There is an experiment. The coin is tossed $n$ times with $p = 0.5$. The experiment is repeated $k$ times. I need to calculate the average central moment. For example, let $n = 5$ and $k = 3$. $[0, ...
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1answer
58 views

Expectation-Maximization Algorithm for Binomial

I have a multinomial distribution with four outcomes, with a pdf: $$p(x_1,x_2,x_3,x_4)=\frac{n!}{x_1!x_2!x_3!x_4!}p_1^{x_1}p_2^{x_2}p_3^{x_3}p_4^{x_4}, \sum_{i=1}^4x_i=n, \sum_{i=1}^4p_i=1$$ The ...
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1answer
255 views

Molecules movement distribution puzzle

Let's say I have blood samples of whiteblood cells ($x$) and viruses ($v$). Space has been discretized in $LL$ spaces. They have a $p_v$ probability of interacting when found in the same space. I want ...
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Which test should I use to determine whether multiple binomial experiments results are different, with p not equal to 0.5 for all? [duplicate]

I have four subject A,B,C,D, I asked 500 students whether they like each subject, there are two choices: Yes/No. I want to test, do students have a preference for any of A/B/C/D? Originally I used ...
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Binomial data: Null Hypothesis $p = 0$ when all Sample Values are 0 - testing and power analysis

I am trying to investigate if the proportion of successes in my population can be shown to be larger than zero. Thus, $H_0: p = 0$ and $H_A: p>0$. Since $p=0$, the prop.test in R does not work, ...
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1answer
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Comparing rates of success in paired groups of samples

I have $2n$ paired populations, on which I measure a rate of success, let's say $(r_{group}^i)_{group \in (0,1)}^{i \in[1,n]}$ where $r_0^i$ and $r_1^i$ are the rates of success in the $i$-th pair of ...
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Generating Binomial Random Variables with given Correlation

Suppose I know how to generate independent Binomial Random Variables. How can I generate two random variables $X$ and $Y$ such that $$X\sim \text{Bin}(8,\dfrac{2}{3}),\quad Y\sim ...
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hypergeometric vs. binomial for sales modeling

Suppose you are selling Product X. You have a customer base with $N$ people. You want to measure the "natural buying probability" (which happens because a customer sees Product X in ads), so you ...
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truncated binomial samples with GLM

We have a binomial process that yields samples of 60 trials. To save time, once 2 failures have been observed the process is reset. So if a test series hits 2 failures early, the resultant sample ...
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1answer
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Non-integer Binomial test equivalent

This is probably a very basic question, but I just can't seem to find the answer elsewhere. If I want to calculate the probability of a certain number of events occurring (say 9 heads out of 20 coin ...
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appropriate binomial proportion confidence interval for repeated measures

So I have looked this up extensively and keep getting the same answer, but its because what I can find online isn't quite to the point. I want to put a confidence interval on a binomial proportion, ...
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Cox/ Binomial Regression: How to reconcile Non-significant model with significant IVs

I'm been performing some survival and regression analyses corresponding to an event of interest being death or a certain surgical procedure, namely a shunt revision for pediatric neuro-surgical ...
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How to interpret parameters of GLM with binomial family for proportions

I would like to use glm with binomial family for proportions. However, I am wondering how could I interpret the parameters that is important in my case. In binary logistic regression one can interpret ...
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37 views

How to estimate probability of $\geq$ n type I error in multiple testing comparison?

My question is about the calculation of the probability of making $\geq n$ type I error when $p$ independent statistical tests are made. I can calculate the probability of $\geq 1$ type I error with ...
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1answer
54 views

Interpreting Cox & Binomial Regression: non-significant Chi-Square values w/ significant wald statistics

Scenario A: In Cox regression, the chi square analysis of the -2 log likelihood (or the omnibus in binomial) is not significant, but some of the values of the Wald statistic corresponding to some of ...
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Is this correct?

There are 40 questions. For each question, there are 5 options of which only one option is correct. 3 points are awarded for each correct answer, and 1 mark is deducted for each wrong answer. For ...
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Ancillary statistic in exact tests

I have been reading about use of ancillary statistic in hypothesis testing. For e.g. To test variance the test statistic is chi sq distributed and is independent of variance. (Please correct me if I ...
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Binomial Distribution vs Poisson Distribution

I don't understand what context should I enable to use binomial or poisson distribution? Any pros and cons for each distribution?
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162 views

Logistic Regression: Bernoulli vs. Binomial Response Variables

I want to perform logistic regression with the following binomial response and with $X_1$ and $X_2$ as my predictors. I can present the same data as Bernoulli responses in the following format. ...
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29 views

Does this variable follow a poisson distribution or a binomial distribution?

I dance an average of 2/7 nights during a week. D = Number of nights dancing in one month/4 weeks. My first thought was Poisson, but am now unsure. Is it none of the above?
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Is a random variable Bernoulli? Is a proof available?

Suppose a die is tossed twelve times and each outcome is represented by a random variable $X_{i}$. Further define $Y_{i}$ for $i=2,...,12$ to take the value $1$ if $X_i=X_{i-1}$ and $0$ otherwise. ...
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Estimates of random effects in binomial model (lme4)

I'm simulating Bernoulli trials with a random $\text{logit}\, \theta \sim {\cal N}(\text{logit}\, \theta_0, 1^2)$ between groups and then I fit the corresponding model with the ...