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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13 views

How does this solution relate to the actual real-life stats problem?

4.62 in Newbold (8 ed): A new warehouse is being designed and a decision concerning the number of loading docks is required. There are two models based on truckarrival assumptions for the ...
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Rule of thumb criteria for number of trials needed to do a binomial test

I have outcomes from a simulation that I expect will exceed a certain number 5% of the time. In order to test if the hypothesis that the probability of an exceedance is indeed 5% I am performing a ...
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Identification of special numbers based on recursive formula (combinatorics)

I am in the middle of a development and I stumbled on recursively defined numbers. They don't ring a bell for me, but maybe they were already studied. Anybody has a hint? $$ \kappa^{(k+1)}_{\delta} =...
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Expected value of binomial distribution with concave utility weighting

I am interested in showing that a function $V(m)=\sum_{j=0}^{m}v({j})\binom{m}{j}\left ( 1-p \right )^{j}\left ( p \right )^{m-j}$ is concave in the discrete sense (i.e., $V(m)-V(m-1)>V(m+1)-V(m)$ ...
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Restricting Binomial Success Rates in simulation

Suppose I am generating 10000 data points with probability P out of N total trials, but I know that P x N can never be below M, where M < N. How would I go about restricting my simulation to never ...
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A regression model for ratio of two Binomial success probabilities

There are two series of observations of two Binomial trials. Observation $i$ of series 1 includes $n_{1i}$, the number of Bernoulli draws and $\overline{p}_{1i}$, the ratio between number of success ...
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Example of setting for binomial distribution with n unknown [closed]

I'm looking for a case example (not necceseraly realistic) with the following properties: data is known to be binomially distributed. parameter n is unknown. (p can be known or unknown) I wish to ...
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How to simulate predicted probabilities

Can you help me out with the following brain twister? I have a prediction model to estimate the probability (p) of a sale for each potential customer. On average, p is 0.003. (So there is approx. one ...
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Shortcut for calculating the standard deviation of a binomial outcome?

We can see the equations for how to calculate the sample standard deviation, and perform these to the sample. If our sample only ever consists of 0s and ...
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Custom Zero-Fail Data Analysis Method

I'm trying to analyze products with zero-failure and get reliability values. I've looked into other methods here. Some of my products have very few observations and some have several hundred. I've ...
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Conditional Probability for Coin Flip Data

I am reading the Tutorial of Fisher Information and it is mentioned that the say we have a random variable $X^n$ where $n$ refers to number of tosses so the RV $X^2$ could be {$1,1$} or {$0,1$} then ...
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Reducing confidence intervals and alpha into a single confidence measure for layperson?

Is there a statistical approach or other practical convention for converting the statistical outputs into a single measure of 'confidence' in an estimate that a layperson can easily interpret? ...
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Binomial experiment with parameters $n = 10$ and $\theta = 1/3$, and denote $X$ to be the number of successes, then $P_\theta(X = 0) = 0.0282$, etc

Chapter 2.1. Classical Definition of the textbook In All Likelihood -- Statistical Modelling and Inference Using Likelihood, by Yudi Pawitan, says the following: Recall first the standard mode of ...
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Generalised Linear Model - Response error is constant; boundary (singular) fit; leading leading minor of order 4 is not positive definite [closed]

I am trying to run the code below in order to simulate P-values using a generalised linear model (power analysis): ...
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Binomial distribution - Question with exercise

I have the following exercise which they give us a hint that the binomial distribution is likely to apply. A company manufactures car components. The quality control scheme for a particular type of ...
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Simulation and sample size [closed]

How to make simulation for very large sample size? Stats:Experts believe that social distancing can reduce transmission of COVID-19 by about 60%. If the total COVID-19 cases all over the world are ...
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Excel's BINOM.DIST different from R's dbinom [closed]

I am verifying some data in Excel and found that Excel's BINOM.DIST function yields somewhat different results from R's dbinom function. The table below shows the first 11 differences when the total = ...
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Which error families are allowed in generalized least squares models?

Which error families are allowed in generalized least squares (gls) models? Can I have, for example, a binomial glm and define a covariance structure (which, I guess, makes it a gls) in it (see below ...
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How many tests should we do to estimate the percentage of people who contracted COVID-19 in Lombardy?

Lombardy, a region of Italy, registered many severe cases of COVID-19 in the last few months. Unfortunately the available data don't allow us to estimate the percentage ...
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Having a hard time with the law of the iterated logarithm

Let's say you have infinitely many i.i.d. Bernouilli variables $X_1, X_2, \cdots$ of parameter $p=\frac{1}{2}$. For instance, the binary digits of a random number. Let $S_n = X_1 + \cdots X_n$. The ...
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Comparison of two scaled binomial or normal random variables

Let $X$ and $Y$ be two independent binomial random variables where π‘‹βˆΌπ΅(𝐾,π‘ž), π‘ŒβˆΌπ΅(𝐾,𝑝) (suppose $p>q$), $a$ and $b$ two real numbers. What conditions can we impose on $a$ and $b$ such that ...
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Probability of a binomial random variable being the maximum of a set of binomial random variables

Let $X, Y, Z$ be independent random Binomial variables, each parametrised with different $p_X, p_Y, p_Z$ but the same $n$. I am interested in a formula for determining the probability that the value ...
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How do I calculate the expected value of a binomial distribution for a genetics example?

I have model with 20 genes which can take on a value of 1 or 0 (the alleles). What is their expected value and variance assuming the alleles are selected with equal probability? Is this just a ...
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How do you approximate the variance for arcsin of a proportion?

I want to calculate the variance of $$\sqrt{n}\arcsin \sqrt{P}$$ and I believe I'm supposed to use the Taylor approximation where $$\sqrt{n}\arcsin \sqrt{P} = Z,$$ where $$Z = g(P).$$ I'm a bit ...
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Is there a connection between the binomial pmf and the formula for entropy? [duplicate]

Many times when two formulas "look" the same, there is some interesting mathematical result linking them. Both the log binomial likelihood and the entropy formula kind of "look" the same, in that they ...
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Hypothesis Test for a Linear Combination of Three or More Probabilities

Suppose that you have a parameter w. As you change the value of that parameter, the probability of a given event occurring increases or decreases. I want to use the Method of Finite Differences to ...
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Statistically analyze path planning strategy effectiveness based on motion samples

My research concerns robot path planning. I want to demonstrate that a robot is more successful using one path planning strategy over another. In these scenarios, two robots are competing, and a ...
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Binomial GLMER and MCMCglmms give opposit sign betas

We did a germinability experiment using 6 species pairs (alien vs. native). We wanted to test how aliens differ from native species in germinability ater controlling for seed traits, such as seed mass,...
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Distribution of a binomial random variable multiplied by a constant

I'm trying to model a process in which a success is the generation of $2$ items. If I model the process using a binomial random variable with p equal to the probability of success, I can compute the ...
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Likelihood of a data point being in one of two binomial distributions

I have two binomial distributions A and B, and a number v. v must belong to either A or B. I would like to calculate the percentage chance v belongs to distribution B. My initial, rather naive, ...
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Expected count of event based on different probabilities per independent day

This is very basic, but I just want certainty that what I'm doing isn't stupid. Say I have a set of data which gives me a probability of an event A happening each day for a week. For example: ...
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Mother milk of 6 Corona-positive (COVID-19) women does not contain the virus - can we make a confidence statement about this?

I am asking this question because I believe it would be great if the statistics community could make a contribution to solving this serious puzzle until more evidence is available. The UK Royal ...
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Converting SAS model to R model: treating intercept as random term

I have a binomial data set in SAS with the following column names: loc, trt, succ, fail I want the response to be the proportion of success, so in my data statement I have total = succ + fail My ...
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What statistical test to use for categorical data with 3 or more groups

We conducted A/B/C test in our website and now i want to check the results. But the problem i faced is that there are 2 test groups and 1 control, and not 1 test and 1 control groups as usual. When ...
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How does the two-sided version binom.test in R work?

For a two-sided hypothesis test, we need to sum both tails when calculating the p-value. For a test statistic that has a continuous and symmetric distribution like the two-sample t-test, this is quite ...
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How to compute $\mathbb{E}[\text{ReLU}(pX-qY)] $ and $\mathbb{E}[pX\mathbb{1}(pX-qY>0)]$ where $X\sim B(K, q), Y\sim B(K, p)$?

Let $X$ and $Y$ are two independent binomial random variables where $X\sim B(K, q), Y\sim B(K, p)$. I am wondering how to compute or estimate the following expectations: $$ \ \mathbb{E}[|pX-qY|]\ \ \...
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Struggling with implementation of Bayesian model (R JAGS)

For more on the background of the model, see my previous question here that describes the context more clearly. In essence, there is a particular Bayesian model that I am trying to implement. Here ...
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How sampling distribution of sample proportion is related to binomial distribution

I am reading a book on introductory statistics. In the book, the author introduces the concept of the "sampling distribution of sample proportion" just after explaining the binomial distribution. I ...
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How to estimate this expectation involving two binomial random variables?

$X$ and $Y$ are two independent binomial random variables where $X\sim B(K_1, q), Y\sim B(K_0, p)$, (Suppose $p>q, p+q$ is not necessarily equal to 1). I am wondering how to compute the following ...
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Majority voting error rate with binomial distribution

We all know that the ensemble error rate for majority voting rule follows binomial distribution (see picture): where p is the error probability of single classifier. However, I have hard time ...
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correlated binomial - default probability of portfolio of two assets with know correlation and different default probability

is there a formula for default probability of two assets with different default probability and know correlation http://fcic-static.law.stanford.edu/cdn_media/fcic-testimony/2010-0602-exhibit-...
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Choosing between two models, logistic regression vs mixed model

I have a dataset, the distribution looks like this, before and after log-transformation. The data tends to separate itself towards two extremes, thus motivating me to classify them as binary and fit ...
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Why am I encountering Error: Response is Constant, when using performing a GLMM using glmer?

I am trying to determine what factors best predict/explain where deer fawns are being killed by predators based on the kill site's distance to clear-cuts (which I've grouped into three different age ...
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Good Book suggestions for model validation statistical tests? (Gini, Kolmogorov-Smirnov, Binomial/Adjusted binomial tests, Chi-square)

Any good books suggestion for the above mentioned topics such as Gini, Kolmogorov-Smirnov, Binomial/Adjusted binomial tests, Chi-square etc. tests?
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Why does using the pnorm function on the intercept estimate of a binomial regression recover the mean of the dependent variable?

I've fit a series of mixed effect models with the lme4 package in r on a set of binomial outcome variables (1: the event happened, 2: it did not). The fixed effect specification is intercept only, and ...
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Explanation of “sufficient statistic” example

I just started learning what a sufficient statistic is: Definition A statistic $T(\mathbf{Y})$ is sufficient for an unknown parameter $\theta$ if the conditional distribution of the data $\...
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Generating unique binomial random variates

Let the set $\{X\}$ be a collection of $n$ iid random samples of $X_i \sim \operatorname{Binomial}(m,p)$. Define $\{Y\}$ to be the set of unique values of $\{X\}$. Is there an efficient method for ...
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Bayesian model: binomial(s) conditional on Poisson

I am struggling a little with how to conceptualize and specify a particular Bayesian model. I suspect the solution is rather simple but for some reason I am having a hard time thinking about this. ...
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why binomial test is considered “nonparametric”?

why binomial test is considered "nonparametric" ? After all it is used to test against an hypotetical parameter p in a binomial distribution, so IT IS about a parameter ! edit:I don't remember ...
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Am I statistically allowed to use a binomial family here -> is my data truly independent?

I'm having trouble with finding the most suitable analysis for my data. I'm investigating the behaviour of wild animals in nature. More specifically, I'm looking at animals scavenging from carcasses ...

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