# 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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### The test point’s standard deviation from the origin (ESL’s Exercise)

This is Ex.2.4 from The Elements of Statistical Learning. I don’t understand the sentence that I underline in the image. I know that $\sqrt{10}$ is approximately equal to 3.1, but I don’t know how to ...
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### Which parameters optimise the weighted cross-entropy loss for a pre-specified categorical distribution?

Question: Given a categorical distribution $C_q$ with parameters $q_1, \ldots, q_K$ with $K > 2$, $\sum_k q_k = 1$, which (new) categorical distribution $C_p$ with parameters $p_1, \ldots, p_K$ ...
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### Testing two proportions of a multinomial distribution

I am wondering if there is a statistical procedure to test if two proportions from a multinomial are equal. For instance: I take a sample of animals in a reserve in South-Africa and count the number ...
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### Generalized Linear Mixed Modeling questions

I have a dataset with assessments taken at different visits: baseline (visit=1), and then various post-baseline visits (2, 3, 4), and the following variables: DISEASE - the outcome, is an ordinal ...
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### Closed form formula for distance of multinomial sample from underlying distribution

Suppose that I have a probability vector $p$ e.g. of size 10, and that I draw a multinomial sample of size $n$ from $p$. Does there exist a closed form formula to compute the expected total variation ...
1 vote
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### Multinomial gam diagnostic help

I have created a Generalized additive model of a multinomial distribution using the mgcv package, I have used check.gam to do some diagnostic tests but they look ...
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### What's the Issue with Modeling Admissions as Multinomial?

I am reading Chapter 4 (Testing and Confidence Regions: Basic Theory) of Mathematical Statistics by Bickel and Doksum. In Example 4.1.1, the authors use the study of sex bias in graduate admissions at ...
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### Determine unknown probabilities from sample of multinomial distribution

Let there be a bag with arbitrarily many balls in k colours (presume we know k). There is a set (but unknown) probability p1, p2... pk of drawing a ball of a given colour. I take a sample of g balls (...
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### What kind of relationship is there, if any, between simultaneous confidence intervals for multinomial proportions and chi-squared residuals?

I'm trying to understand if/how the chi-square test relates to simultaneous confidence intervals for multinomial proportions. It doesn't relate to a practical problem to solve, so this is just a ...
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### Distribution of vector of $n$ Bernoulli trials

I have a random variable $X\in\{-1, 1\}^n$ that is just a vector of length $n$ containing either $-1$ or $+1$. I know that $\rho$ is the probability of the event $X = +1$. I would like to describe the ...
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### How to test null hypothesis with partly confounded multinomial dependent variable

I have independent sample data consisting of 12 levels, where the dependent variable is multinomial with three possible outcomes corresponding to Strategy 1, Strategy 2, and Strategy 3. Each level is ...
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### Multinomial mixed effect regression?

I have data regarding level of damage in tissue samples, using a Likert scale. Our main goal is to understand if there is a difference in the levels between two groups - control and treated. An ...
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### Response variable (Before,during, after) is it ordinal or multinomial?

Hi I am looking at elemental concentrations in pectoral fin rays the year before spawn, year of spawn, and the year after spawn. I will be creating a logistic regression model to see if I can predict ...
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