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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continuous vs discrete random walk

For 1D random walk in discrete case the probability of finding walker at position X after N steps(P_N(X)) is binomial distribution(http://mathworld.wolfram.com/RandomWalk1-Dimensional.html), moreover ...
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27 views

How to find the probability that a group of people is not allowed to enter a country given some factors?

I have this scenario: There are two countries A and B. A sends a group of N people to B... There is an independent probability of p that a person gets fatigued while traveling to B. And I have ...
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Beta as distribution of proportions (or as continous Binomial)

Beta distribution is related to binomial being also the distribution for order statistics. Probability mass function of binomial distribution is $$ f(k) = {n \choose k} p^k (1-p) ^{n-k} \tag{1} $$ ...
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confidence interval for proportion

Suppose $k$ events were observed in $n$ trials. We then have $\hat{p} = k/n$ and the standard Wald confidence interval is $$\hat{p} \pm z_{\alpha/2}\sqrt{\hat{p}(1-\hat{p})/n}$$ I wonder why the ...
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8 views

Probability of Pr(N=0) as function of Panjers (a,b) parameters

Is there a way to find the general formula for Pr(N=0) as the function of Panjers parameters a and b for Binomial, Negative Binomial and Poisson distributions? It is possible to show e.g. parameters ...
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3answers
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Bayesian inconsistency

I have a small knowledge of Bayesian analysis which I want to apply to invert some instrumentation data which has a complex nonlinear response. However this simple example confused me so before I go ...
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29 views

The expected correlation from a mixture of binomial distribution

I am working on a particular mixture model of the following form: $\frac AB =\frac CD$, where I am mainly interested in the correlation between both ratios. I have done several simulations that show ...
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2answers
93 views

Combining Binomial Random Variables

(Disclaimer: This is not a homework question). I am trying to teach my self some elementary probability, and I thought of this following example: Imagine you are playing a game involving two coins. ...
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19 views

binomial test for two data populations

I have a test that has 39 questions. 20 of them have 18 possible answers and 19 of them have 3 possible answers. I built a QA system that answers 19 of the 20 and 18 of the 19 correctly. I want to ...
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1answer
18 views

Binomial test for nested data

I have 100 subjects who were scored on their performance in a series of trials (binary outcome for each trial: "hit" or "miss"). I want to find out whether overall there are more "hit" than "miss" ...
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1answer
61 views

How to determine posterior distribution of the parameter in a binomial

Assuming that I performed n iid tests, and the total number of test is n which is a fixed value, and the observaton of 1 which corresponding to successful results is X observations yeild with ...
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Repeated measures binomial effect confidence intervals

I have a repeated measures study design with two separate conditions in a memory task where one must recognize previously seen items in a list. The conditions are concrete vs. abstract. I'd like to ...
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Cumulative Binomial Distribution

I need to show that B(x; n, p) = 1 - B(n - x - 1; n, 1 - p) in which B is a cumulative binomial probability (B(x; n, p) = sum from k = 0 to x of b(k; n, p) for x = 0, 1, 2, ..., n). The solutions to ...
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23 views

Covariance in binomial distribution

Is the covariance between number of success and failure in a binomial distribution with parameters n and p, the same as the covariance between two binomial variables, which is -np(1-p)?
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Binomial test with replicates

I have RNA-seq data that I'd like to test for allele-specific expression, and I have three biological replicates. For an individual locus, I have thousands of sequencing reads, and my null hypothesis ...
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1answer
78 views

Probability of a rare event

Let's say I consider an event rare if it occurs no more than once in 90 days. Assuming everything is random and independent, If I see this event on day 3 of the observation, what is the probability ...
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Normal approximation of parameter $p$ of $Bin(n,p)$? [closed]

I've seen normal approximation applied for approximating a binomial distribution $B(n,p)$. However, if one estimates the parameter $p$, then can the parameter $p$ be "normally approximated" just as ...
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35 views

Use of “mean” in estimating $p$ of $Bin(n,p)$?

The $p$ (probability of success) parameter of binomial distribution $Bin(n,p)$ can be estimated by deriving it from the mean: $$\mu = np \iff p = \frac{\mu}{n}$$ However, given example that r.v. ...
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Bernoulli trial on Poisson random variable

I am trying to assess the sensitivity of an electronic system under alpha radiation. In "dynamic" mode, the system performs different kinds of operations (without any pause) which might fail due to ...
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55 views

Variance in estimating p for a binomial distribution

how can I calculate the variance of p as derived from a binomial distribution? Let's say I flip n coins and get k heads. I can estimate p as k/n, but how can I calculated the variance in that ...
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16 views

Power of a binomial based test

I have a Bernoulli trial, which by definition can be either success of failure, and I have a Binomial random variable of the number of successes, where I don't know p (I wish to estimate it). I have a ...
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25 views

Buckets of dice - Binomial probabilities of either event occuring

I'm doing a bit of analysis on a dice rolling mechanic for a role playing game. This is a buckets of dice system where the result is based on the count of the number of dice rolling a given target ...
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1answer
29 views

How to compare to failure rates when one process has zero failures?

I have produced 50 units and after testing, I notice that 3 of them have a failure. So I change my production process and produce another 50 units. This time, I detect no failures. Did I resolve the ...
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Why is a larger sample required for a weaker rate when the response is a binary event?

I am interested in conducting an experiment and am attempting to calculate the sample size required for this experiment. If I hold beta at 0.8, alpha at .95, and am looking for a 5% increase, why do I ...
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15 views

Average likelihood in coin flipping game

Alice plays Bob in a coin flipping game where both are handed possibly unfair coins (coin $i$ has $p_i$ probability of landing as a head, $i = \text{A}, \text{B}$). Both Alice and Bob are going to ...
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1answer
28 views

Standard error on an estimate derived from 2 estimated proportions - Survey data

I have survey data where I want to calculate a derived variable, based on 2 estimated proportions. (e.g., "Did you visit the web-page?" If Yes, "Did you place an order?", and I want to estimate total ...
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200 views

Visualize bivariate binomial distribution

Question: what does a bivariate binomial distribution look like in 3-dimensional space? Below is the specific function that I would like to visualize for various values of the parameters; namely, ...
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27 views

How to calculate the probability p of a binomial distribution using the mean?

You are given following elements about a binomial distribution: n = 15 $\overline{x} = 2$ What is the value of the probability $p$? I mean this $p$: My guess is: $p = ...
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1answer
20 views

How do you compute the beta-binomial probability of “at least one”?

When working with the binomial distribution, it's sometimes useful to compute the probability of "at least one", which is 1 - P(none) or, after setting x to 0 in the formula for the PDF of the ...
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1answer
39 views

fitting a binomial glmer or an lmer to a proportional response variable

I'm hoping somebody can help with what I think is a relatively simple question, and I think I know the answer but without confirmation it has become something I just can't be certain of. I have some ...
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29 views

Bernoulli process of not-fixed probability p?

Here's a question that might be basic, but I want to understand what distribution(s) would result when the underlying Bernoulli trials' probability $p$ varies with time...?? I assume that it's not the ...
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7 views

Interim Analysis for Futility in a 1-Arm Trial with a Binomial Outcome

I am planning a 1-arm trial that tests a response rate in patients to a drug. The response rate indicative of the drug working would be 30%, and 10% would be considered the null response rate (i.e., ...
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Degrees of freedom - binary vector

I came across the following statement: A general distribution over a binary vector (of lenght N) has $2^{N}-1$ degrees of freedom, whereas a factorial distribution over a binary vector has only N ...
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Fitting binomial regression model in R - correct formula, significance testing, and over-dispersion

I'm using generalized linear models to test for the effect of various predictors on some binomial data. My response is a binomial vector of successes and non-successes. I want to test whether my ...
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contrast testing in binomial GLM when variance = zero

I am trying to use GLM (family = binomial) to to test for differences in gene frequency among treatments. The data is binary (gene is present or absent). Its a simple one way model,but with quite a ...
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154 views

Unable to reproduce paper results (sample size)

I am interested in using the results from this paper (Modified exact sample size for a binomial proportion with special emphasis on diagnostic rest parameter estimation by Geoffrey Fosgate) to ...
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200 views

What sort of GLM should I use if my response variable is colony size?

I want to model mean colony size as a function of predator density. Within each treatment level the smaller colonies (3-5 individuals) are a lot more common than the large ones (up to 600 ...
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1answer
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Understanding the Binomial distribution better

This might be a super novice question you'll all laugh about, but you have to be brave if you want to seek knowledge! So here we go: Let's say there's a medical test that's 99% accurate. Let's say ...
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Statistical testing, and example about critical area

So I do not understand one part of the answer to the following question, here it goes from the beginning : A coin is thrown $100$ times and it is counted the number of times heads and tails come up. ...
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1answer
42 views

What is the minimum sample size for an exact binomial test of goodness of fit (two-tailed)?

I am doing a two tailed exact binomial goodness of fit test, see, e.g., here. I am looking for something similar as for Chi-square tests, which, as a rule of thumb, require a frequency of 5 for each ...
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44 views

Probability Questions within R

I'm learning about Probability with Binomial, Poisson and Normal Distributions. I came across some study examples on-line that ask you to do it within R. I was given 10 exercises which were: I did ...
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35 views

Combining additive and multiplicative effects in logistic regression

I want to figure out how to do a logisitc regression (alternatively GLM w/ logit link) where some featured affect the output linearly (additively) while others affect it multiplicatively. That is, ...
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1answer
32 views

Confidence interval from R's prop.test() differs from hand calculation and result from SAS

I'm wondering if anyone has insight into how prop.test() in R calculates its confidence intervals. Although it doesn't state it explicitly in its documentation, my ...
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1answer
26 views

Binomial Probability of Success Given Probabilities of Individual Words in a Phrase?

If I have aggregated statistics on individual words of a phrase, is there a way to compute the overall probability of a phrase having a "success" vs "not success" (binomial)? Example Phrase: ...
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1answer
34 views

First and second moments of deep nesting of the Binomial-Binomial hierarchical model?

I am interested in the Binomial-Binomial hierarchical model, where the number of trials itself follows a binomial distribution. I would like to know the expected value (first central moment, $\mu_1$) ...
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29 views

Standard Deviation vs. Standard Error of Bernoulli Trials

There is a related question and clear answer here: http://stats.stackexchange.com/a/11542/22088 But my question is slightly different. I posted a comment but the answerer has not been on Stackexchange ...
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Modelling A->B or B->A relationship

I am trying to model the order in which two events (A and B) happen. That is, for a sample I know that, A->B happens 500 times B->A happens 350 times I ...
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28 views

Probability question about sample proportion

This question goes, "According to a study, 4% of a population in a region have lung disease. Of those people without lung disease, 13% are smokers. Of those people with lung disease, 92% are ...
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Why isn't it 'wrong' to use a log link instead of a logit one when doing GLM with a binomial family?

I am taking a basic biostats class for an epidemiology masters and we were recently told that log-binomial GLM is what we should be using instead of logistic regression because the coefficients are ...