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.

learn more… | top users | synonyms

0
votes
0answers
12 views

Convert probabilities of “binomial events” into beta distribution for binomial parameter (theta)

I have three events that essentially arise from a binomial distribution with k=2, i.e., X~Binomial(theta,n=2). Given some model and data I obtained a conditional (pos distribution for a particular ...
0
votes
0answers
7 views

Collaborative filtering when ratings are spare bon

I have a matrix (User X Item) of binomial estimates of click through rates. That is, each entry in the matrix is the estimate of the probability that a specific user will click on a specific target, ...
1
vote
0answers
16 views

Binomial, as N goes to infinity

I live in a world of size $N$. There are $U = uN$ many urns, and $B = bN$ many balls. The likelihood of any particular urn having $k$ many balls is given by $f_N(k, n=bN, p=(uN)^{-1})$, where $f_n()$ ...
3
votes
0answers
26 views

Test of strict difference in independent binomial probabilities

Suppose $X,Y$ are two independent binomial random variables with parameters $n_1,p_1$ and $n_2,p_2$ respectively. Suppose one wanted to test the hypothesis $p_1>p_2$. Conditional on $X+Y=s$, ...
2
votes
1answer
35 views

Does sampling from a larger sample change how much variance around an estimate to expect?

Suppose you have one billion marbles. Each marble is either red or white. Call the proportion that are red, p. You randomly sample 100 marbles. Based on this sample you estimate $\hat{p}$. You can ...
0
votes
0answers
14 views

Statistical validity of association rules with low support

We have data sample with 10,000 observations. We are using association analysis to find segments with low support (< 4%) and high(er) confidence. Our rules are always in such way that on the right ...
0
votes
1answer
20 views

Distribution of partially observable binominal parameter

I suspect this is a textbook question but I don't seem to have the right textbook. Anyway I am trying to estimate probability of coin landing on heads, p, by repeatedly flipping it N times, i.e., ...
-1
votes
0answers
17 views

comparing more than 2 groups of different size having binary values

I have 4 groups (Group 1, Group 2, Group 3, Group 4) that could be seen as binomial distributions. The groups have different sizes and the elements of each group can assume [0,1] values. Each group ...
0
votes
0answers
7 views

How do you deal with overdispersion in a zero-inflated negative binomial regression AND when you expect data to have zeros?

Background: I am analyzing the effect of multiple variables (lineage, ancestral plant species, plant species reared from, larval density, body mass) on different traits: ovigeny index (initial egg ...
0
votes
0answers
41 views

Test of Equal Proportions with exact p-values [duplicate]

The question "Test of Equal Proportions with zero successes" showed me that using a test of equal proportions with very low or very high numbers of successes doesn't give an accurate p-value. Below is ...
0
votes
0answers
13 views

Fitting a Fractional Logistic Model using GLM in R

I have a response variable that is a proportion bound between 0 and 1. I would like to fit a fractional logit model using R. I've consulted a few posts on crossvalidated and stackexchange and came up ...
3
votes
0answers
56 views

Test for difference in proportions with small probabilities

I want to perform a test for differences between 2 binomial populations. The probabilities are small (usually less than 10 %). I can define the successes as "rare events". I think that the z-test ...
1
vote
2answers
42 views

Convergence of moments of binomial to Poisson

As is well known, the $\mathsf{Binomial}(n,p)$ distribution converges to the $\mathsf{Poisson}(a)$ distribution as $n\rightarrow \infty$, $p\rightarrow 0$ with $np=a$. I'm pretty sure that the ...
3
votes
2answers
179 views

Why are there huge differences in the SEs from binomial & linear regression?

I have data from a simple experiments where people put (a fixed number of) balls either to the left or to the right of them (each ball is just the same with regards to consequences of putting them to ...
0
votes
0answers
15 views

Comparing likelihoods of different experiments

Call $X_{i,j} \sim B(p_{i,j})$ a set of independent coin tosses with parameters $\{p_{i,j}\}_{i,j}$ where $j\in[1,p]$ and $i\in[1,n]$. In plain text, all the coins are biased in a different way. ...
1
vote
1answer
32 views

Can I do a Binomial test on more than one individual/group? Can a repeated t test have different sample sizes?

I've conducted an experiment on chickens, training them to associate either blue or yellow with a 30 or 1 second wait before a food reward and then giving them a preference test, 15 times in total and ...
0
votes
0answers
41 views

Probability of observing an excess of $k_0$ points via a binomial distribution with the isotropy assumption

Consider an area $\Omega$ and its subset $\Omega_1$. Let the hypothesis be that the distribution of points in the area $\Omega$ is isotropic. That means that a probability of finding a point in the ...
0
votes
0answers
17 views

what's the right way to combine binomial parameter estimates?

let's say you have a bunch of weighted coins. by observing flips, you can estimate (a confidence interval for) the binomial parameter for each. how should you combine these to summarize the ...
4
votes
3answers
326 views

Is the Standard Deviation of a binomial dataset informative?

I am working on a dataset of presence/absence data, with my response variable being 'proportion of sites where X is present'. I have been asked to provide standard deviations alongside the mean ...
4
votes
1answer
43 views

Bayesian inference with unequal sampling

I have a "two-column" data set, with a multi-class categorical variable A, and two-class variable B. It is assumed that each observation is independent. For each category of variable $A$, I want to ...
1
vote
0answers
20 views

Distinguishing two Bernoulli random sources

I have a source of independent Bernoulli random variables, which is either $(X_i)$ or $(Y_i)$ where $\Pr[X_i=1]=p$ and $\Pr[Y_i=1]=q$. I can sample as many values as I'd like, and would like to figure ...
1
vote
1answer
43 views

PCA on count-based data

I'm looking to do a PCA analysis on count based data itself rather than averages. I'm hoping this will help for variable observation depths; for example, 3/4 reads is not really equivalent to 15/20. ...
4
votes
1answer
152 views

Name of single sample multinomial distribution

The Binomial$(n, p)$ distribution is called "Bernoulli distribution" with parameter $p$ in the special case $n=1$. Many properties of the Binomial are derived from the fact that the sum of $n$ i.i.d. ...
2
votes
0answers
61 views

Can I use Bayes Theorem to find a conditional distribution rather than conditional probability?

I might be going about this the wrong way, but I'm trying to develop an understanding of a particular conditional value, say $P(CustomerBuysFries | CustomerBuysHamburger) = P(F|H)$. Ultimately, I want ...
0
votes
0answers
10 views

Variance of the logarithm of a binomial distributed random variable

What is the variance of $\log(1+X)$, where $X \sim Bin(n,p)$. I am looking for an approximate solutions depending on n and p. I have tried Taylor expanding the logarithm, but it didn't lead to a ...
1
vote
0answers
10 views

Estimate growth rates in a probit/logit model

I consider a situation where k different kinds of bacteria grow together in a petri dish and each kind of bacteria exhibits exponential growth, i.e. the population size over time is given by $N_i(t) = ...
1
vote
2answers
23 views

Hypothesis test for mutually exclusive samples from a single population?

Let's say I gave 100,000 people a survey on their favorite fruit, where they can bubble in "Apple" or "Pear" (but not both). They can also leave it blank. The results are 90,000 people left it blank, ...
0
votes
0answers
9 views

Is the beta binomial with a variance equal to almost zero equal to the binomial distribution?

I was wondering whether the following holds: if I have a certain average and an almost zero variance and I use them to estimate the alpha and beta for the beta binomial distribution. Would that be ...
0
votes
0answers
22 views

Reimplement Binomial Test R-> Python

I am trying to re-implement a Binomial test in R that uses the alternative= "greater" optionin Python using scipy. Right now I am looking at ...
0
votes
0answers
34 views

click through rate stats

I have a group of 10 users. Each user receives a daily notification for one week. Ideally, each user will click on all notifications received. At the end of the week I collect the number of clicks per ...
2
votes
1answer
31 views

Understanding binomial distribution in iris recognition

I'm trying to understand, how the solid curve on the plot here was produced. The legend states that it is a binomial distribution, but as far as I know, this distribution produces integer numbers from ...
0
votes
0answers
29 views

is it ok to use binomial test for google analytics' conversion?

I have been thinking on one issue and would like to know if it is correct reasoning? In Google Analytics conversion is defined as number_of_transactions$/$number_of_sessions, one session can have ...
0
votes
0answers
35 views

How to calculate the probability of no show rate in airlines

At present I am analyzing the historical airlines data which has got the information of bookings and no shows. Now,to calculate the probability of no show rate,is it simple percentage or is there any ...
0
votes
0answers
52 views

Accounting for overdispersion in binomial glm using proportions, without quasibinomial

I am doing binomial GLM using relative abundance, for example: model<-glm(cbind(number_pres,number_abs)~Var1+Var2+Var3+Var4..., family=binomial, data=Data). My sample size is about 700, and I have ...
3
votes
1answer
114 views

Statistical comparison between binomial distributions, two groups and many trials

I have a data set with two groups. I have multiple trials with different Ns in each trial, and different numbers of trials for each group. In each trial, for each ...
0
votes
1answer
47 views

Testing for differences between populations of individuals with binomial data

So I am trying to compare between populuations and determine whether there is a difference in count based data. My data look like this: ...
2
votes
1answer
48 views

Variance of compound distribution

The binomial distribution describes the probability of $k$ 'success' events given $N$ independent trials, each with a probability $p$ of being a success. The distribution is described by the formula ...
1
vote
1answer
29 views

Minitab question about binomial probabilities [closed]

What I have tried: My first instinct was to go to Calc>Binomial distributions> Binomial to get the graph of it. 2 questions: What does the question mean it needs values less than 21? Should ...
1
vote
0answers
9 views

Binomial Logistic regression to Compare results of multiple methods to a known value

I have a "known value" (recorded by a field observer) which I want to compare several methods of data collection with to test for significant differences between methods. Methods: 2 points along a ...
5
votes
2answers
59 views

How do I include measurement errors in a Bernoulli experiment?

I would like to understand how to combine a known measurement error in a Bernoulli experiment with the confidence interval in order to calculate error bars. I am performing an experiment that has two ...
2
votes
1answer
49 views

A simple question about MAP and MLE

I recently got this simple question from a friend. But I am quite confused about it. Suppose we toss a coin $N$ times, and got heads $m$ times. Assume the binomial distribution with $p$ which is the ...
0
votes
0answers
20 views

How to address the problem of underdispersion in a binomial GLM (data in proportions)

We explored the effect of seed size, and seed-coat thickness on seed removal rates (proportion of seeds removed) and seed predation rates (proportion of seeds preyed upon)by rodents. Seed size was a ...
1
vote
4answers
126 views
4
votes
1answer
80 views

Berry-Esseen bound for binomial distribution

From the Berry-Essen theorem I can deduce $$\sup_{x\in\mathbb R}\left|P\left(\frac{B(p,n)-np}{\sqrt{npq}} \le x\right) - \Phi(x)\right| \le \frac{C(p^2+q^2)}{\sqrt{npq}}$$ with $C \le 0.4748$. My ...
8
votes
1answer
356 views

Why doesn't a sample proportion also have a binomial distribution

In a binomial setting, the random variable, X, that gives the number of successes is binomially distributed. The sample proportion can then be calculated as $\frac{X}{n}$ where $n$ is your sample ...
2
votes
2answers
55 views

Relation between power and sample size in a Binomial Test?

$\beta$ (also called sensitivity or power) is a function of the sample size. It totally makes sense to me when we're performing a regression for example. The intuition is not that clear when we ...
1
vote
1answer
29 views

Analyzing binomial distributed variables

I have the following situation. A subject comes to the clinic at day 1 and is evaluated using a 10 item checklist. The sum of those 10 items is the subjects score. A intervention is performed. The ...
0
votes
1answer
38 views

Calculate the average rate of success

It sounds like a simple problem but I am unsure about the methodology I should follow. A company developed processor with a new innovative way and they tested the processors to see if they pass the ...
2
votes
1answer
41 views

LRT for one-sided Bernoulli parameter

Suppose $X_1,X_2,...,X_n$ are i.i.d. $\mathrm{Bernoulli}(\theta)$. We are interested in testing the hypotheses $$H_0:\theta\leq\theta_0$$vs. $$H_1:\theta>\theta_0$$ Show that if we use the ...
1
vote
1answer
113 views

R: prop.test - Chi-squared approximation may be incorrect

I am trying to compare the proportions of two populations, using prop.test My data is straightforward - first population is 6/26 and second is 15/171. I am trying ...