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

1
vote
0answers
24 views

Finding a Scalable Approach to a modified coin-flip problem using MLE model

and thank you in advance for your help! I am interested in applying MLE to estimate parameters in a "modified" coin flip model, but have been having difficulties scaling the solution. The problem ...
0
votes
0answers
30 views

Quantitatively analyzing relationships between multinomial and multiple binomial variables

I’m analyzing crowdsourced Twitter data, where workers labeled tweets. Within my dataset (N=2,400), I have one IV (call it ‘ds’) with 2 levels that differentiates which dataset the workers labeled. I ...
4
votes
1answer
34 views

Multiple binomial variables: probability they are all 1

We have observed four phone booths by recording, at a given time point, whether each phone booth is occupied (0 or 1). We have approximately 50 such observations (i.e. at 50 different time points, so ...
0
votes
2answers
34 views

Logistic regression with only categorical predictors

So I started off with a model which included both continuous and categorical predictor variables. But now I wanted to drop the only continuous variable (distance to shore), because to my opinion it ...
0
votes
0answers
13 views

Binomial Hypothesis Test Segmentation For Webpage A/B Testing

My Question: Is page1 performance better or worse than page2 performance? Which page would you switch traffic to? More Context ...
3
votes
1answer
33 views

Link functions for Binomial Regression

So I have a dataset of presence (1) and absence (0) data, but it mainly consists of 0's (~80% of the 5200 observations). Now while constructing my binomial logistic model I am reading (Zuurt et al. ...
1
vote
0answers
28 views

Binomial modelling, testing and Bonferroni

I am currently trying to validate an implementation that is supposed to randomly assign a certain number of tags to users who enter a platform. The variable of interest here for me is the sum of all ...
0
votes
0answers
19 views

Model design and nonconvergence problem with GLMM, incomplete block design in R

I have a two-part question that includes issues with generalized linear mixed models and failure to converge. First, a little bit about my experimental design. I have data where I am trying to test ...
0
votes
1answer
33 views

How to test whether two coin replicates are both biased in one direction?

Assume we have two coins replicates, which are produced in the same pipeline. To test whether the coins replicates are both biased in one direction (e.g. the probability of head > 0.5), we did flip ...
6
votes
0answers
78 views

Prediction interval for a future proportion of successes under Binomial setting

Suppose I fit a Binomial regression and obtain the point estimates and variance-covariance matrix of the regression coefficients. That will allow me to get a CI for the expected proportion of ...
0
votes
1answer
34 views

Writing a function in R that imitates rbinom [closed]

I'm just learning to write functions in R for the first time and I'm trying to mimic the rbinom() function in R. I've written some code but I'm not sure if it is repeating what rbinom() does. Also how ...
0
votes
0answers
19 views

Interpretation of GLMM output

I have an output ("summary()") of a GLMM ("lme4::glmer()") but I am not quite sure how to interpretate the estimate values of the fixed effects. My response variable is binary and all independent ...
0
votes
0answers
6 views

What statistical test should be used to compare two independent samples over time (pre- and post-test) for binomial variables?

A typical question is: Do you have a paid job? 1 Yes 2 No I have a treatment group and a comparison group (not matched--in fact they're quite different from each other) and I'd like to statistically ...
-1
votes
1answer
14 views

Warnings using lme with a binomial distribution

Good morning all!I am trying to run a binomial gmler model. My response variable is a binomial variable: extra pair paternity -->( 1 or 0) I am looking at several continuous variables like weight, ...
1
vote
1answer
31 views

Can this situation really be modeled using a Binomial Random Variable? It seems we're sampling without replacement

I've seen the following situation modeled using a Binomial RV: We know that 20% of the people living in a village are against building an airport while 80% are in favor of it. If we randomly pick a ...
1
vote
0answers
40 views

likelihood for binomial proportion

A man must evaluate the proportion $\pi \ (0 \leq \pi \leq 1)$ of diesel vehicles crossing a road. He notes the first 10 cars arriving and records 3 diesel vehicles. I know that $f_Y(y;\pi)\sim Bin(\...
0
votes
0answers
6 views

Appropriate to interpret logistic regression interaction when DV probability is the same for two cells?

I have two factors (F1, F2) and I want to determine if they interact. A possible problem, however, is that the probability of the outcome occurring is exactly the same for two of the 2x2 cells (b-a ...
1
vote
0answers
6 views

Residuals for zero bounded data

So, I'm running into an interesting problem with my residual plot. For reference, I'm trying to model a response variable "exploration" for a social network. Exploration is the number of people you ...
1
vote
1answer
24 views

Fitting data to binomial or bernoulli distributions

I'm trying to fit a count variable to discrete distribution, poisson and negative binomial are not the best candidate to my data since i have only 3 possible values: 0,1 or 2 (sometimes 2) . Can ...
0
votes
1answer
19 views

Accounting for interval censoring JAGS model of binary mortality data

I have data on tree mortality, based on two observations of a tree in time. All trees are alive at the beginning of the interval. The length of the re-measurement interval, ...
3
votes
0answers
24 views

Wald confidence interval with delta method

Using the delta method, show that the Wald confidence interval for the logit of a binomial parameter $\pi$ is $$\log \left(\frac{\hat{\pi}}{1-\hat{\pi}} \right) \pm z_{\alpha/2} \sqrt{\frac{1}{n\hat{\...
3
votes
1answer
49 views

Relationship between Poisson, binomial, negative binomial distributions and normal distribution

When we have to define discrete counts distributions, we usually use : Poisson distribution, if mean = variance Binomial distribution, if mean > variance Negative binomial distribution, if mean <...
-1
votes
1answer
39 views

Negative probabilities - what are the two ordinary pgfs that correspond to the gf of a half-coin?

In Half of a Coin: Negative Probabilities, author considers pgf of a fair coin represented by random variable, $X = 1_H$: $$G_X(z) = E[z^X] = \sum_{x=0,1} z^xP(X=x) = (z^0)(1/2) + (z^1)(1/2) = \frac{...
0
votes
0answers
15 views

Calculate relative standard error with binomial proportion?

If one has a rule that says, do not report an estimated mean if its relative standard error exceeds 30% as that estimate is considered "unstable"[1] or "reliable"[2] how does one deal with a binomial ...
0
votes
0answers
6 views

Weighted binomial confidence interval in Stata [migrated]

I am trying to compute a binomial confidence interval for a dummy variable after specifying the survey design in Stata with the svyset command but I get the ...
2
votes
0answers
39 views

The marginals of a truncated multinomial are truncated binomials?

The multinomial distribution for a vector $\vec x$ of non-negative integers assigns a probability of: $$f(\vec x) = n!\prod_i p_i^{x_i}/x_i!$$ to every vector $\vec x$ of non-negative integers in ...
0
votes
1answer
16 views

What is chance performance cut-off for a 2-part dichotomous response?

If subjects had to give 2-alternative forced choice responses for a task (Y/N) and then rate the certainty of their response (also 2-alternative forced choice: High/Low), and we analyzed their ...
1
vote
0answers
28 views

Probability of a Blizzard - Poison vs Binomial vs Bayesian

My goal is to model data I have collected to compute the probability of a severe blizzard occurring in a given set of states (region). Assume the US is broken into 3 regions that categorize the ...
0
votes
0answers
36 views

How to combine/pool binomial proportion confidence intervals after multiple imputation?

After I multiply imputed my dataset m times I wanted to calculate a binomial proportion confidence interval. I did that formerly using the Hmisc::binconf() function ...
2
votes
0answers
56 views

Probability than empirical mean of one binomial RV smaller than another

Lets suppose I have two binomial random variables: $X \sim B(n_1, p_1)$ and $Y \sim B(n_2, p_2)$. I would like to calculate the probability than the empirical mean of $X$ be smaller than the empirical ...
3
votes
1answer
66 views

What is the probability that the matrix is orthogonal?

Let $X$ and $Y$ be independent $Bin(3,\frac{1}{3})$ random variables. Then what is the probability that the matrix, $$ P=\begin{bmatrix} \frac{X}{\sqrt2}&\frac{Y}{\sqrt2}\\\frac{-1}{\sqrt2}&\...
2
votes
1answer
43 views

binomial distribution and rolling dice

I play a tabletop game and we roll dice for game outcomes. The dice have 8 sides and a certain result (lets call it a success) appears on 2 sides, so 25% of success. If I roll 4 dice, the chance of ...
0
votes
1answer
15 views

Error Rate Confidence

I have a very basic understanding of statistics and have the following question: Given a test that can be run and give either a Pass or Fail result, how do I calculate how many times I must run the ...
1
vote
2answers
31 views

Expected number of points in k turns?

I'm not too familiar with expected values so I'm wondering if people could verify if I'm on the right track with my thought process here. If the probability of winning one point in a turn is 1/9, ...
2
votes
2answers
28 views

Binomial proportion statistics for variable $n$?

Using the standard definition of the sample proportion random variable: We first suppose $X \sim binomial(n, p)$ is the count of "successes" in $n$ trials where each trial has probability $p$ of ...
4
votes
2answers
86 views

Integration of product of functions of “x” with exponents/powers (binomial problem)

Original problem: A point X is randomly chosen from the interval (0,1). Suppose X=x is observed. Then a coin with P(Heads) = x is tossed independently n times. Let Y be the number of heads in n ...
2
votes
0answers
29 views

Limiting distribution of $\frac{\bar{x}-p}{\frac{pq}{n}}$ from mean of $Bin(1,n)$?

I found some difficulties in here. We know that if $X$ has Binomial distribution with $1$ trial and $p$ success, or what we called $X$~$Bin(1,p)$, we have $\mu=p$ and $\sigma^2=p(1-p)=pq$. From that, ...
1
vote
0answers
33 views

Beta binomial GLMM dispersion statistic issue

I am analyzing proportion data with GLMM in which the number of occurrence a behaviour of interest has been displayed and has not been displayed are concatenated and fitted as a single response ...
2
votes
1answer
63 views

What is the probability of the first positive event in an sequence of binary events where sequences have finite but random lengths?

I have a time series of observations from a longitudinal study of individual objects. These observations are seen as discrete sequences of features, one sequence per object. The sequences have ...
0
votes
0answers
21 views

Interpretting Confidence Interval Questions

Q.In a survey conducted by a mail order company a random sample of 200 customers yielded 172 who indicated that they were highly satisfied with the delivery time of their orders. Calculate an ...
3
votes
2answers
69 views

Product of binomial probability

I am trying to get an estimate for the Drake Equation by simulation (context doesn't matter to this question) I have reached a point where I have a number of planets, $n_e$, and 3 probabilities; $f_l,...
1
vote
1answer
20 views

Extracting Standard Errors for a combination of factorial predictors in binomial GLM

Suppose I run a binomial GLM (in R) with response variable [0,1] and 2 predictor variables that are both categorical. Let's call them a and ...
0
votes
0answers
12 views

Using variables measured at different scales in a binomial GLMM with successes and failures

I have seed and seedling abundance data for several plant species. I am trying to model the effect of my treatment on how many seeds successfully transition into seedlings (seed-to-seedling ...
1
vote
1answer
29 views

Removing intercept from GLM for multiple factorial predictors only works for first factor in model

I am running a binomial logistic regression with a logit link function in R. My response is factorial [0/1] and I have two multilevel factorial predictors - let's call them a and b where a has 4 ...
0
votes
0answers
11 views

Consecutive sampling from a pool

I am new to stats. I have a straightforward ball drawing situation. If I have certain red balls (r) among blue balls in a pool (total: N), and I sample the balls with replacement for a certain times (...
1
vote
1answer
16 views

Uncertainty in a fractional count

What is the uncertainty (68% confidence level) of $N/M$, where $N$ is the number of entries that pass a cut and $M$ is the total number of entries? ($N$ and $M$ are both integers, and I'm interested ...
2
votes
0answers
100 views

Unbiased estimator of binomial parameter

Let 4,3,5,2,6 are 5 observations of the binomial(10,p) random variable.What will be an unbiased estimate of $(1+p)^{10}$ ? I have tried to solve the problem in this way. We know that $E[\frac{\bar{(...
0
votes
0answers
9 views

how to test multiple binomial events

Suppose I have a million coins, they have different propabilities for heads, and I known the probability of each of them. Now, I flip each of them once and record the head/tail events. How can I test ...
0
votes
1answer
15 views

Alternatives to Google's weighted sort for binomial experiments with n=1

An interesting data scientist interview question: "We are looking at the failure rate for opening files on websites for many clients. We want to rank the files by failure rate; but, with our current ...
0
votes
1answer
20 views

Poisson regression with offset vs logistic regression

I am thinking to use Poisson regression with an offset variable instead of a logistic regression in case where event is rare, since p (probability of success) is very small and n (sample size is large)...