Questions tagged [binomial-distribution]

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.

Filter by
Sorted by
Tagged with
0
votes
0answers
24 views

Completeness calculation: Where does the $\sum_{i = 0}^n g(i)$ in $E_p[g(T)] = \sum_{i = 0}^n g(i) {n\choose{i}} p^i (1 - p)^{n - i}$ come from?

I have the following definition of completeness: Definition Let $Y_1, \dots, Y_n$ be an i.i.d. $f_\theta (y)$, where $\theta \in \Theta$. A statistic $T(\mathbf{Y})$ is complete if no function $g(T)$ ...
0
votes
2answers
33 views

exact binomial test with power calculation that excludes the lower limit of a 95% CI

In a regulatory document I see the following statement and wonder how the sample size of 141 subjects is calculated: A sample size of 141 subjects provides 80% power to exclude a response rate of 12% ...
1
vote
0answers
25 views

Is this tennis player a fraudster?

In this article Anhörig vann 270.000 kronor – tennisspelare åtalas för mutbrott it is claimed: It seemed that she intentionally hit double errors or lost points on occasions in the match so that she [...
0
votes
1answer
31 views

Likelihood function for number of slots taken over slots available

I have a study in which I am comparing the number of outpatient visits a certain surgery experiencse in a same period in two different years; the total number of visits is a limited by the number of ...
1
vote
1answer
27 views

What is the name and formalism of this discrete distribution? [closed]

I am searching the name of something similar to a binomial distribution, but with individual probabilities (P(1) to P(N)). I calculated (brute-forced with a script) the probability of k positive ...
3
votes
1answer
58 views

Does a Binomial converge to Poisson or Normal?

I have read the answer here. Here the distinction is that If $n\to\infty$ and $p\to0$ while $np$ approaches some positive number $\lambda,$ then the binomial distribution approaches a Poisson ...
0
votes
0answers
41 views

Confidence interval for combined populations

I'd like to compare two approaches for calculating the confidence interval ($CI$) when estimating the mean for a sample of weighted values: The first approach is based upon the standard error of the ...
0
votes
0answers
32 views

Deriving Gaussian from Binomial?

Just for the sake of curiosity, I've been curious if the Gaussian distribution was derived from the Binomial, or if it was found by other means, and retrospectively associated with the Binomial. ...
3
votes
1answer
39 views

Binomial GLMM with proportions and categorical predictors

Study background My research question looks at the effect of age group (AgeGr) on gazing. Each infant was observed for 1h and signals with gazing (...
0
votes
0answers
10 views

The tail distribution of a binomial distribution can be expressed in terms of an appropriate beta distribution function - Explanation [duplicate]

I was reading the paper: "Estimating Probabilities of Default for Low Default Portfolios" by Katja Pluto and Dirk Tasche and they mention the following: The tail distribution of a binomial ...
1
vote
1answer
16 views

Binomial vs hypergeometric finite sampling distribution

I was reading these notes:Finite Population Sampling with Application to the Hypergeometric Distribution and I have a question just about the first two pages. The first page, they derive the variance ...
2
votes
1answer
28 views

Binomial hypothesis test for $p_1 = p_2 = P$ without normal approximation

I was testing whether the proportion of successes from two populations is the same. It made me realize I only know how to do this with a normal approximation. In particular, I would like to solve ...
4
votes
1answer
56 views

Hit probability of a motif in DNA sequence

I am trying to figure out expected number the occurrences of a DNA motif in a sequence. Let me first show a small example for the base case: Assume we have a DNA sequence 'TACCTG', where in every ...
1
vote
1answer
16 views

binomial vs betareg? glm for y=ratio

https://docs.google.com/spreadsheets/d/1e_XOgTv1flSFFleHSwUJJPBzBdd9VPXRaZc2oukwtrE/edit#gid=0[data][1] I'm using glm to evaluate the response of mammal species to different % of forest cover. My ...
0
votes
0answers
6 views

Distribution similar to binomial that can account for changes in variance due to sample size?

Imagine that I am measuring successes and failures where p=0.5 and sample size = n. The problem is that I know that with increasing n, the variance of the success or failure measurement also increases,...
1
vote
1answer
20 views

Intuition or proof for combinatorial function in binomial distribution

For a the probability of a binomial distribution with n trials, the probability of k successes where Prob(success) = p is (n Choose k) * p^k * (1-p)^(n-k). I understand that we have to multiply p^k * ...
1
vote
0answers
8 views

One-sample: difference between two proportions that are parts of the same whole

What is the sampling distribution of the difference between two proportions when they are parts of the same whole. It's relatively easy when one proportion is binomial, the one of the common ways to ...
1
vote
1answer
19 views

Covariance between a binomial random variable and its size (number of trials) (found in the context of binomial thinning)

Assume we have a random variable $X$, and we construct another random variable $Y$ to be from a binomial distribution of size $X$ and success probability $\alpha$, i.e., $Y \sim Binom(X, \alpha)$. How ...
4
votes
0answers
68 views

How does Pfizer justify it's Beta-Binomial model?

This is a bit of a hodge podge of different clinical trial related questions, but starting with some basics. It seems like they're defining vaccine efficacy differently depending on where you look. At ...
1
vote
1answer
28 views

How to compare a population proportion to a probability of success of 1?

I would like to assess whether my population proportion (P1) is significantly different from a hypothesized value (P0). I would usually use a binomial test to test this hypothesis. However this time ...
0
votes
0answers
18 views

What type of statistical test should I use?

I'm running an experiment to try and analyse how often people punish those who betray a group. We made a choose your own adventure type game and got people to play it. It simulates a secondary school. ...
0
votes
1answer
38 views

Finding a confidence interval for difference of proportions

Let two independent random variables, $Y_1$ and $Y_2$ that have binomial distribution have parameters $n_1 = n_2 = 100$, $p_1$ and $p_2$, respectively, be observed to be equal to $y_1 = 50$ and $y_2 = ...
0
votes
0answers
8 views

Specific probability value of a posterior distribution?

I'm dealing with Bayesian design study. Currently I'm facing with an issue where I was asked to compute the probality that the posterior distribution of the risk complication/mortality rate in the ...
0
votes
1answer
34 views

Adding of two confidence intervals

Given two variables $\bar{A}$ with 95% confidence interval [$A_0$,$A_1$], and $\bar{X}$ with 95% confidence interval [$X_0$,$X_1$], how would one calculate the 95% confidence interval of a composite ...
0
votes
1answer
30 views

Binomial Hypothesis testing finding p value

Question: how to find a p-value where: $H_0: \hat{p} = 1/6 $ $H_a: \hat{p} \ne 1/6 $ Significance level is $\alpha=.05$. In my test: $n = 60$, $x = 14$, so my $\hat{p}=0.2333$. How do I find a p-...
0
votes
0answers
11 views

What is “Distribution-specific variance” or σ2d

I've built several binomial mixed effects regression models and always get the same "distribution-specific variance" (=3.29). In the 'help' of tab_model() it says the following: ...
5
votes
2answers
114 views

Why is the variance of a binomial distribution not $n^2p(1-p)$?

Using properties of variance, we know that $Var(aX)$ is $a^2Var(X)$. A binomial distribution has n many Bernoulli trials, i.e. we can substitute $Var(X)$ with $Var(nB)$ (where $X$ is a binomial ...
0
votes
0answers
29 views

Do I have a censored variable or not? What is the mean of my data?

I have a variable variable from a survey, which has a range from never (0) to always (100) in 10 steps (0 -100). It is obviously a discrete (ordinal) variable, but I want to try to treat is as ...
1
vote
0answers
9 views

I need help to choose between GLM and LMM or GLMM

I have a dataset of 200 subjects, who were divided into a control arm and a treatment arm (100 per arm). I am investigating the incidence of pain above a certain threshold, so i was thinking if using ...
1
vote
1answer
10 views

Establish confidence / error for multiple contingency tables with dynamic outcomes

In a task, a participant sees two types of prompts, 1 and 2. The participant might answer A or B. The participant might give an answer that cannot be coded as A or B, we treat these as missing data. ...
1
vote
0answers
10 views

Calculating a covariance [duplicate]

Consider two stochastic processes: $T_t$ is the number of times we flip a coin with bias $\rho$ by time $t$, and $X_t$ is the number of heads of the coin by time $t$ (i.e. after $T_t$ flips): $$T_t \...
0
votes
1answer
45 views

How to estimate probability of $\geq$ 1 success from a non-IID vector of probabilities, given many such vectors (now with asteroids)

I've got a deep neural net that returns sequences of probabilities. There are 25 probabilities per sequence. Many of these probabilities are zero, as a result of padding; when the input to the ...
3
votes
3answers
108 views

MLE estimator for the second parameter of binominal distribution

Let us have a sample $X_1, X_2, ... , X_n$ with $B_{p,m}$ distribution. How to make an estimator for $m$ using MLE ? For simplicity, let us $n=1$ I am a little bit stuck, because I have a derivative ...
3
votes
1answer
38 views

Citation for Joint Density of Poissons Conditioned on Sum

We are interested in the joint density of two Poisson distributions conditioned on their sum: $$ P(X_1=n_1,X_2=n_2|X_1+X_2=n) $$ Where: $$ n_1 + n_2 = n $$ I am looking for a citation supporting the ...
2
votes
1answer
38 views

Can Student's t-distribution be used in Normal Approximation to Binomial?

The question nearly covers it all. I clearly have a binomial distribution, however the variance and standarddeviations are unknown, the population is also just ...
0
votes
0answers
74 views

GLMMs with no intercept to test means of factor levels against zero

I want to analyse binomial accuracy data generated under four different conditions with a binomial generalized linear mixed-effects model using the lme4 package in ...
1
vote
1answer
24 views

Issues with using GLMM to fit binomial dataset with sites nested within sub-watershed nested within larger watersheds

I am looking to fit a glmm for a project dealing with the presence and absence of a species of fish. I have been reading up on mixed modeling with hierarchical nesting and thought I had a decent grasp ...
0
votes
0answers
16 views

generalized linear mixed effects model mathematical equation

I am fairly new at statistics and I am faced with a problem of not understanding what it means and how would it look like in R script. Can somebody explane it to me? We use a generalized linear mixed ...
1
vote
1answer
41 views

Analysis of binomial variables with random effects

I have a study where each of the 43 items is a question to which the response may be A or B and I want to infer whether A has been chosen significantly more than B. There are 20 participants and 43 ...
2
votes
1answer
48 views

Alternatives to binomial test when the observations are not independent

In my experiment, participants had to choose between two possible answers (say A and B) for different (40+) questions. I want to test whether option A is chosen more frequently than the alternative; I ...
1
vote
0answers
15 views

Conf intervals on the dispersion coefficient of quasibinomial GLM or binomial GLMM with obs-level random effect

In this post I see how they calculate the confidence interval on the theta parameter of a negative binomial GLM: Confidence Interval for the Dispersion parameter of negbin distribution. I typically ...
1
vote
0answers
40 views

Possibilities for rolling two dice: one is six-sided and the other one is four-sided

I have seen a question from someone's old exam. Two dice, one has 6 sides and the other 4 sides. Question: a) What is the probability that the possible outcome(sum of two dice) would be at least 9? ...
0
votes
1answer
26 views

Coverage of a Bootstrap Confidence Interval for a Change in a Binomial Proportion

How can I estimate the coverage of a bootstrap confidence interval for a change in a binomial proportion please? For example, if the results from two tests (A and B) are: ...
0
votes
0answers
8 views

Finding the maximum of an experimental parameter for ensured success

Summary of the problem I have an experimental setup on which I measure one parameter and either get success or failure for each experiment. I can execute as many experiments as needed. I want to find ...
0
votes
0answers
14 views

A Binomial distribution of which the number of trials is a Poisson distribuion [duplicate]

It is known that X is a random variable which follows Poisson distribution Po(λ), Y is a random variable which follows Binomial distribution Binomial(X,p). The problem I encountered is: Proof that Y~...
0
votes
0answers
16 views

Obtaining estimated probabilities and 95% confidence intervals from binomial GLMM

I have a dataset where I am testing whether, overall, individuals are more likely to mate (mating_response) with individuals of the same type rather than a different type . The response variable is ...
0
votes
1answer
18 views

Significane versus null hypothesis for small number of data

I have a model that correctly identifies something seven times out of the finite number of 8 data points as true. I was wondering how can I calculate a significance statistics given the very low ...
1
vote
1answer
16 views

Distribution of R|R+T for R,T binomials with the same probability

$$R \sim \mathrm{Bin}(N_R, p)$$ $$T \sim \mathrm{Bin}(N_T, p)$$ What is the distribution of $R$ given particular value of $R + T$? My guess would be that $R | R + T \sim \mathrm{Bin}(R + T, {N_R \over ...
4
votes
1answer
105 views

Multinomial & Covariances

Assume we have $\mathbf{X} = (X_1,\ldots,X_k) \sim Multinomial(n,\mathbf{p}=(p_1,\ldots, p_k)).$ How can we find $\operatorname{Cov}(e^{X_i},e^{X_j})$? Tried to do CLT but it's led me nowhere.
0
votes
1answer
136 views

Linear transformation of a binomial random variable?

Let $X$ be a binomial random variable with parameters $n$ and $p$. Next, let: $$ Y = aX + b $$ I know that: $$ \mathbb{E}[Y] = \mathbb{E}[aX+b] = a\mathbb{E}[X] + b = anp + b \\ \text{Var}(Y) = \text{...

1
2 3 4 5
40