Questions tagged [multinomial-distribution]

A multivariate, discrete probability distribution used to describe the results of a random experiment where each of $n$ outcomes are placed into one of $k$ nominal categories.

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How to calculate the combinations probability of X>values given a frequency distribution

Lets imagine I have the following distribution of values: Value N Cases % 0 60 60 1 20 20 2 10 10 3 8. 8 4 2. 2 Assuming independence of events and no order: What is the probability of a ...
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Variance and co-variance of bivariate multinomial distribution

Suppose we have two discrete variable $(X,Y)$, where $X$ takes values $x_i, i=1,2,...,k$ and $Y$ takes values $y_j,j=1,2,...,l$. Suppose we have total $n$ samples of $(X,Y)$, let random variable $Z_{...
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Find the Fisher information matrix for the MLE of a Multinomial

Please help me how to find the Fisher information matrix for the MLE of a Multinomial... It is said that considering n and p constraints in multinomial distribution. In other words, when p has k-...
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How to plot confidence intervals for multinominal logit predicted values in R?

I am going to use UCLA example on multinominal logit as a running example. I want to analyze the predicted probability of each response based on social-economic status (...
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MLE of categorial distribution with two restrictions

Suppose that $X_1, X_2, \dots, X_n$ is an iid sample from a categorial distribution with $k\in\mathbb N$ events. That is, the probability that $X$ is equal to some $x\in\{1,2,\dots,k\}$ is given by $$...
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How to derive the determinant of the variance of a negative multinomial distribution?

The probability mass function of the negative multinomial distribution is: \begin{align*} \mathbb{P}(\boldsymbol{\rm{X}}=\boldsymbol{\rm{x}}|\mathbf{p})=\frac{\Gamma\left(x_0+\sum_{i=1}^{m}x_{i}\right)...
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Detecting statistically significant change between multinomial samples and individual category proportions

Say I have a categorical variable with more than two categories, e.g., a person's country of origin. Assume the number of categories is some finite $k$ (e.g., not dealing with distribution of people'...
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What would be a likelihood ratio test based on nested multinomial logistic regression models for one-sample testing of categorical distributions?

(Let’s assume a multinomial distribution with a size of just one, so a categorical distribution: either dog, cat, or alligator.) I have done multinomial two-sample tests a few times lately, and I’ve ...
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Statistical Test for multinomial distribution

Suppose there is a multinomial distribution $X \sim Mul(p_1, ..., p_k)$ and I have $n$ samples, where $n_i$ samples gives the first category, .... Then, the sample mean are $\hat p_1 = \frac {n_1}n, \...
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How to determine sample size when performing indirect sampling?

Problem Summary I want to know the minimum sample size needed for a given confidence level and margin of error when performing indirect sampling where samples from the two populations are not one-to-...
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Bayesian updates for Dirichlet-multinomial with Gamma prior

Let $$ \begin{aligned} X_i &\sim \text{Dir-multinom}(X\mid\lambda)\\ \lambda_{j} &\sim \text{Gamma}(\lambda_j\mid\alpha,\beta)\\ \end{aligned} $$ where $i$ iterates over observations, $j$ ...
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Pairwise comparisons for probabilities from multinomial model

Q. How can I do pairwise comparisons for probabilities and associated CI's obtained from a multinomial model? The simple example. We have been conducting some experiments for sediment preference for ...
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Why do proportions hold across credibility range in multinomial distribution? How to compute probability of deviations from that?

I know I can use pymc3 code like this to find out if die is biased and what side is it that is more prone to show up (taken from here). ...
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Multinomial logistic regression for proportions in R

I am asking myself the following question: Is a multinomial logistic regression adequate to model a proportion Y_n/Y? f.ex.: Y_n = number of broken phones, divided by Y = number of total phones sold X ...
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Fitting a multinomial glm for a very large dataset

I have compositional data where for two groups, where each is represented by two ages, there are 100 possible categories for which I observed counts: ...
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Multinomial Logistic Regression vs. Logistic Regression Results in R

I am running multinomial logistic regressions in R using the multinom function from the nnet package. Most of my variables are categorical, and oddly almost all of the variables come out significant. ...
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Multinomial with small counts and many cells

I have data distributed as multinomial, with $N= 1,000$ observations divided among $n=10,000$ cells, with unequal probabilities $p_i$, for $i=1,...,n$. I would like to assess how likely it is that an ...
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Why multinomial regression gives huge difference in Odds Ratio when variable treated as continuous and tertile categories?

I am trying to perform a multinomial regression model with the values of Leptin against BMI levels (Normal, Overweight and ...
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Probability that two samples from a multinomial distribution intersect in a specific way

The following combinatorially difficult problem has obvious applications in information retrieval and bioinformatics but I haven't seen its solution discussed anywhere. I am interested in computing ...
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Confidence intervals for multinomial proportions

I know that there are a lot of methods to find the confidence intervals for binomial proportions using methods like Agresti-Coull, but is there any important papers mentioning to find confidence ...
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Question about paper on Bayesian Shrinkage Estimation

I am reading the paper Bayesian Shrinkage Estimation of the Relative Abundance of mRNA Transcripts Using SAGE, and I am trying to work out the calculations for the complete conditionals for the Gibbs ...
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A regression in R with a categorical response variable

I have a conceptual question. I have a dataset with a categorical response variable (integers from 1 till 10) and numerical predictors (independent variables). I want to be able to predict the value (...
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Question about a mixture dirichlet MCMC model

I am self-learning Bayesian statistics using the book Computational Bayesian Statistics by Turkman et al. and I am currently stuck on Chapter 6 Problem 10. It can be found here on page 124. I am ...
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One-vs-rest vs one-vs-one multiclass probability validation: does it matter?

Now that I have figured out how rms::val.prob works to the extent that I have written my own Python implementation, I would like to extend that idea to multiple ...
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"Cumulative distribution" of a collection of random variables with different distributions

I am working with an application where I have a grid of cells, and I calculate "concentrations" in each cell by randomly placing a number of "particles" across the grid, and ...
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BASIC: Probability of a box to contain n-keys

Consider the situation in which 4 boxes exist, as well as 4 keys. Each key is stored inside of a randomly chosen box. Now suppose we chose a box at random. What is the probability of the chosen box to ...
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Multinomial test from finitely many possible multinomial distributions

my area of focus is within pure math, but I've found myself in a situation where I need to run some sort of statistical test, and I am hoping someone can point me towards the correct test or framework....
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How to choose alternative specific constant (ASC) in multinomial logistic regression in R? (unlabeled choice experiments)

I am trying to replicate my colleague's NLOGIT analysis using R. This analysis was for a discrete choice experiment in which fisherman chose whether to opt into a hypothetical environmental protection ...
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EM algorithm for multinomial data

Good afternoon , Assume we have a dataset modeled by multinomial data of K cluster. To apply EM algorithm parameters are : $${\theta }^{\left(0\right)}=({p}_{k}^{\left(0\right)},k=1,\mathrm{\dots },K)$...
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Distibution of the number of trials required to see all possible outcomes

In the simplest case given a set of N items is the distribution for the number of draws with replacement before all items are seen? This is the case I really need. More generally what is the ...
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Modelling Fixed and Random effect using 'glmer' function with response variable having 4 categories

I am doing doctoral study where I am trying to model 'Human - Wild Animal Conflict'. My response variable is Type of Injury sustained (4 Categories from Low to High Injury). Predictors are mix of ...
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Power Calculation for Annotating Data

I need a power calculation for annotating data. We draw from a database of customer complaints with two separate labels. One for the product and then another for the customer's complaint. We change ...
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Implementing Multinomial Logistic Classification

I have a dataset that has probability labels instead of one-hot-encoded labels AND I'd like to keep it that way. The probabilities of each sample is information that I'd like to influence the loss ...
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Latent class Analysis covariates in prior and differences in distribution family for the response variable

I am trying to identify the level of risk in some municipalities in Colombia based on violent events using a latent class model. I have two response variables, one based on actual violent events (...
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Likelihood and multinomial distribution notation trouble

I was asked to prove that dirichlet distribution is conjugate for multinomial distribution but I'm not sure what the notation below which I was showed really means: $x_1,...,x_k|\theta_1,...,\theta_k \...
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Logit-Poisson Trick

Consider an analysis of discrete-choice logit, where the independent variables vary with the alternatives. Suppose that each individual is represented once in the sample, and that different ...
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Difference between multinomial distribution with n trials and categorical distribution performed n times

I want to understand if there is any difference between performing multinomial distribution with 1 trial, 10000 times and performing multinomial distribution with 10000 trials, 1 time. Here is the ...
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Estimating covariance of multimodal distribution from series of samples

I have two random variables $X$ and $Y$, the variables are distributed multimodally. I want to calculate covariance $Cov(X, Y)$ from a series of batches of data. For example I have a series $X_1 = \{x^...
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How to get overall p-value in multinomial regression after MICE on R

I run multinomial regression after multiple imputation in R. This is a GEE multinomial model with a survey design : ...
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Expected 0-1 under multinomial distribution

Suppose the world generates a single observation $x \sim \text{multinomial}(\theta)$, where the parameter vector $\theta = (\theta_1,\ldots, \theta_k)$ with $\theta_i\geq 0$ and $\theta_1+\ldots+\...
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Is this possible: Estimate the probability that a specific outcome for a categorical variable is possible based on a sample of observations

So I have this challenge and I am not sure if it is possible to solve with statistics. So anybody with some ideas which directions I should look into, would be great. Assume I have a categorical ...
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Building a Multinomial Logistic Regression Model

My DV is dichotomous. One component is binary (Y/N) while the other is a spectrum (3 Likert scale question that their z scores were summed up. All predictors are categorical. Control variables include ...
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When sampling a categorical distribution with $k$ outcomes of equal likelihood $n$ times, what is the probability of sampling all categories?

Suppose I have a multinomial distribution with $k$ categories and $n$ trials where the probabilities of each category are the same ($1/k$). I would like to know the probability that every category has ...
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Joint distribution of data sampled iid from a bernoulli process, and the absence of binomial coefficient

Let's assume I have 4 observations with each observation is modelled as a bernoulli trial with probability $p$. Sucesses are labelled as 1, failure is 0. My observations $(x_1, x_2, x_3, x_4)$ are as ...
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Using the bootstrap for estimating the odds ratio standard error

I have the following table $$ \begin{matrix} &R = 0 & R = 1 \\ E = 0 &n_{00} &n_{01}\\ E = 1 &n_{10} &n_{11} \end{matrix} $$ If needed, this is census data from a metropolitan ...
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The proper test statistic for variables which are functions of multinomials

This may be very basic but I'm drawing a blank and google isn't helping ... In an A/B setting I'm comparing two random variables $X_a$ and $X_b$. $$ X_a = \frac{\sum X_{ai} * C_i}{\sum X_{ai}} $$ and $...
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Cumulative sums of two competing multinomial distributions

Related to this: https://math.stackexchange.com/questions/1977628/dice-roll-cumulative-sum Take an example of turn-based RPGs. $A$ and $B$ are two competing game entities, with hit point totals $n_A$ ...
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How to sample $n$ observations from a multinomial distribution using binomial (or poisson) sampling?

Context I have $n$ observations which I'd like to sample with replacement for the purpose of bootstrap. A way to think about it is that we have a multinomial distribution with $n$ classes and that we'...
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What is the distribution of the difference of two independent multinomial random variables?

Say I have two independent random vectors $X_c$ and $X_f$. The random vector $X_c$ is composed by three random variables: $X_{1c}$, $X_{2c}$ and $X_{3c}$. The second random vector $X_f$ is composed by ...
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Independent / joint / multivariate negative binomial distribution

I'm not sure what variation of the negative binomial distribution is most suited to use. Say I have a bag of balls of m different colours, I draw n balls from the bag and want to model x_1, ... , x_m ...
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