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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analyzing binary mortality data collected at different remeasurement intervals. Bonus for R implementation

I am replicating an analysis that models tree mortality data. Data are structured such that forest sites are revisted at some random interval, which is recorded. It is then determined if a tree lived ...
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7 views

One sample test or 2 sample test [on hold]

Pepsi is marketing, too see which one people like better coke or Pepsi. we know there are 19 people, and 11 choose Pepsi and 8 choose Coke Initial hypothesis is qp=.5 and alternative is 9 is not ...
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17 views

Show stopping time $T$ has finite expectation by finding an upper bound for $P(T=k)$

Given random variables $$X_1, X_2, \ldots \stackrel{iid}{\sim} P(X_i = 1) = p = 1 - q = 1 - P(X_i = -1)$$ where $p > q$ in a filtered probability space $(\Omega, \mathscr F, \{\mathscr F_n\}_{n ...
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16 views

Why is multinomial variance different from covariance between the same two random variables?

We know that if $\big(X_1,X_2...X_k) \sim multinomial(n;p_1,p_2...p_k)$ then $X_i \sim bin(n;p_i) $ Then, $var(X_i) = np_i(1-p_i)$. But we have $cov(X_i,X_j) = -np_ip_j$. So doesnt that imply ...
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How many boxes have balls?

I have N boxes, each of which may or may not contain a ball. I want to know how many boxes have balls by sampling the boxes in the following way. For each box in the N boxes: I open this box with ...
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24 views

Nonlinear regression vs. GLMs for estimating ED50

Are binomial GLMs better than nonlinear regression for model-fitting, and predicting ED50s and other effective dose point intercepts? In toxicology it is typical to run an experiment with a ...
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9 views

Strange predictions from binomial glmm?

I am analysing the dominance of a Species, i.e. its relative abundance in a community. Since these data are proportions I use binomial models. However, the predictions from these models are ...
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2answers
44 views

What transformation should I use for a bimodal distribution?

I have some bimodal data like the one generated down (R language), and I don't know how to transform it to have a normal distribution or homoscedasticity. I'm running a linear discriminant analysis ...
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1answer
24 views

Generating Random Variable from Binomial Distribution [closed]

I am using r for generating random numbers from Binomial distribution using the following code: ...
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91 views

Probability of a claim being rejected or accepted using binomial distribution

I am self-learning statistics. I was going through Probability and Statistics For Engineering and the Sciences by Jay L. Devore and stumbled upon the following example: An electronics manufacturer ...
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28 views

68–95–99.7 rule for binomial distribution?

What I want to calculate is the probability that the size $k'$ of an intersection of two subgroups with sizes $n$ and $K$ that have been randomly selected from a group with size $N$ that is smaller ...
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24 views

How to derive bernoulli deviance

I found the deviance definition in https://en.wikipedia.org/wiki/Deviance_(statistics) and the one-observation bernoulli deviance in Scikit Binomial Deviance Loss Function. $$ ...
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1answer
50 views

Beta approaching Binomial

If we have a Beta likelihood and a binomial prior, we get a beta posterior. Can someone please explain why this approaches a binomial as $n\rightarrow\infty$. I plotted it and this appears to be the ...
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8 views

Estimated values for Chi-square

To test if my point pattern is random, I am going to conduct a Chi square test. The data has 40 points divided to 3 by 3 tiles. Should I use Binomial or Poisson probability to calculate expected ...
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1answer
36 views

normal approximation to the binomial distribution: why np>5?

Nearly every text book which discusses the normal approximation to the binomial distribution mentions the rule of thumb that the approximation can be used if $np\geq5$ and $n(1-p)\geq 5$. Some books ...
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Looking for derivation of Shannon entropy of binomial distribution

According to Wikipedia, the Shannon entropy of a binomial distribution is $\frac{1}{2}log_2 (2\pi*e* np(1-p)) + O(1/n)$ Does anyone know where I can find a derivation?
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1answer
28 views

Exact binomial test. Directional hypotheses - how to explain differences in results?

Let's assume the following problem: A sample of 30 subjects has been drawn from a specific population. It has been proved that the expected rate of some negative events among the subjects in ...
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19 views

How to interpret glmer results based on a bootstrap dataset?

I have bird nesting data and I am trying to see whether the nest treatment has any significant effects on the survival of the nestling. My original data set is relatively small (n=101). The response ...
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18 views

Comparing binomial outcomes from prediction algorithms in R

I've written a simple model to predict the outcome of soccer games based on some input. The outcome is either "H","D",or "A", short for home team, away team, or draw. I'm comparing the results of this ...
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20 views

How to deal with 2 response variable model?

given, for example, a glm model: fitglm <- glm (formula = cbind(Successes, Failures) ~ other variables, family = binomial) How would you interpret the ...
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22 views

Confidence interval for estimator of the mean of different binomial distributions

I have a dataset that is a series of binary matrices like so: 00000 01110 00110 00000 Each matrix is sampling from the same distribution. I'm aggregating the 2D ...
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19 views

GLM model specification in distribution and link function for fractional (percentage) response data

I have some aggregated data. Indep. Dep. N 1.3 78% 23 1.2 67% 20 Note that both the independent and dependent variables are aggregated by ...
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1answer
50 views

Standard Error differences Binomial Regression vs Poisson Regression

I'm running three different models on a dataset found in table 9.1 of Dobson's Introduction to Generalized Linear Models textbook. Model 1 is a poisson regression, Model 2 is a binomial regression ...
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15 views

Offset instead of percent data?

In R I want to build a GLM explaining the fraction of a coral perimeter that is covered by different algae. I measured the perimeter of the coral (in cm, integer values) and fraction that is contacted ...
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1answer
31 views

Can there be overdispersion in a logistic regression model where each observation represents a single Bernoulli trial?

A friend and I are having a dis-agreement about over-dispersion in binomial/logistic regression glm modelling. We have structured our data so that each observation represents 1 Bernoulli trial (so the ...
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14 views

Compare two distributions with varying focus on different regions

I have been trying to find if my problem matches has been discussed in prior research and if any technique exists to solve it. Here's the problem: Given two distributions (pdf) D1 and D2 over a ...
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42 views

Basic Binomial distribution computation

first post on this website. I have a very basic question on computing a somewhat large computation. The equation to be solved is as follows: $$P(X<262) = \sum_{x=0}^{261} {5236 \choose ...
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3answers
60 views

Why doesn't multiplication by constant affect MLE? [duplicate]

I have an example that derives the MLE for Binomial. Since there's that factorial term $n_i \choose x_i$ in front of the Binomial p.d.f. and it's a constant, the example claims that one can merely ...
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1answer
29 views

Expectation of a function of a binomial distribution

I have a question that is: Given n iid Bernoulli(p) distributions: $X_1, X_2, \ldots, X_n$ and $S_n=\sum X_i$. Find $E[(S_n-np)^3]$. Hint: $S_n-np= \sum (X_i-p)$. So far, I have gotten that $S_n$ is ...
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32 views

Best sample size formula and continuity correction for tiny proportions?

I have found the following formulae (from http://www.itl.nist.gov/div898/handbook/prc/section2/prc242.htm) to estimate the sample size required to test the binomial proportion in a single sample. I ...
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10 views

What is the best test to measure deviations from tiny proportions?

What is the best (most reliable and robust) test to measure deviations from tiny expected proportions (e.g., p0 < 10^-6) in a huge sample? Binomial? Poisson? Negative binomial? Something else? ...
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22 views

Sample size to test small proportion

What sample size $n$ is required to test the following binomial probability in a single sample: $H_0: p \leq p_0$ $H_1: p > p_0$ Is there an exact, robust formula to calculate $n$ in terms of ...
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Do I have binomial data, and how do I treat it?

I have field observations that are essentially presence/absence, but here are the details: randomly placed quadrats are divided into 10 squares. The field data recorded are the number of squares which ...
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1answer
371 views

How to find correlations between multiple low-frequency variables?

Let's say we have multiple ($k > 2$) binary variables (e.g., genetic mutations and/or disease states), which appear at a given frequency of $f(1)$ to $f(k)$ in a sample. We would like to test ...
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175 views

Why do small sample sizes give more significant p-values for rare events?

Maybe I'm getting a bit confused, but I have a single binomial variable with very low frequency (e.g. 1 event in 100,000 trials), and I'm trying to figure out what sample size is required to show a ...
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9 views

Sample size for binomial test with ultra low frequencies?

What sample size is required to determine whether there is a significant deviation from the binomial distribution, where positive cases occur with ultra low frequency (e.g., 10^-6)? Is there an exact ...
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1answer
43 views

Exact Binomial Test p-values?

I get the same p-value for a one-tailed and two-tailed exact binomial test for some combinations of x, n, and p. Does anyone know why this happens? What formula does R use to calculate the p-value for ...
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8 views

Can Fisher's exact test be used with more than 2 binary variables?

Can Fisher's exact test (and the associated hypergeometric distribution) be used with more than 2 binary variables in a 2^k contingency table? Or is there some equivalent test and distribution to ...
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10 views

Sample size to determine correlation between multiple binomial variables?

How can I calculate the sample size to test for a correlation (p < alpha) between multiple (k > 2) binomial variables, where the frequency f of each variable is very low? For example, what sample ...
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76 views

Best way to measure correlation between multiple (>2) binomial variables?

What is the best (most simple and robust) test statistic to measure the overall degree of association (inter-dependence, correlation or covariance?) between multiple binary variables? I have been ...
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1answer
33 views

Some questions on multiple logistic regression

Let's say we have k binary (binomial) variables, and a sample size of n observations per variable, where each variable occurs (positive case) at a given frequency/probability f. We would like to check ...
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46 views

R binomial GAM weight

My aim is to fit a binomial GAM and I wish to weight my presences and absences equally. When using decimal weights I get the following warning: "Error: In eval(expr, envir, enclos) : non-integer ...
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61 views

Sample size formula for multiple regression between binomial variables?

Let's say we have k binomial variables, and a sample size of n observations per variable, where each variable occurs (positive case) at a given frequency/probability f. We would like to check if ...
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1answer
19 views

Expected number of outliers in repeated series of coin tosses

Out of a theoretical population of $200000$ players who theoretically each play a $1000$ games, each with a chance to win $0.5$, I would like to know how likely it is we see players than win $700$ ...
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3answers
202 views

Probability of n-bit sequence appearing at least twice in m-bit sequence

Lets assume that we have a pattern $\alpha$ of bits of length $n$. Then I wish to know what the probability is of $\alpha$ appearing on a string of bits of length $m$ at least twice (where $m > ...
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1answer
25 views

underdispersion in a binomial GLMM

I am trying to analyze data from an experiment in which I measured the learning of a colour preference in birds under two treatments. 40 Individuals were organized into 8 groups, and 4 groups were ...
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69 views

Negative-Binomial vs Poisson for Count Data

Say that I was modelling the number of upvotes for a Facebook post under two treatments. What would be a more ideal distribution for modelling these counts: negative-binomial or a Poisson? What would ...
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60 views

Not sure how to solve this, whether to use Gaussian or Bernoulli

Sorry for the incorrect formatting, my first time posting here. So I've got the following question - the probability of A is 0.2. Given 5000 trials, what will be the variation from the expected ...
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1answer
50 views

Estimating proportions & 95% CIs with clustered data from very few clusters

What are the best method(s) to estimate a proportion and its associated 95% confidence interval (ideally with an option for an exact method to avoid values +/- 100 or 0) when the data are clustered, ...
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65 views

Power Analysis By Simulation

Problem : A simulation of power gives a far more conservative sample size to just using power.prop.test in R (say). Question : Is the simulation we are using a reasonable way to estimate power. Are ...