We've got 1 shorthand for multinomial distribution »
Acronyms that contain the term multinomial distribution
What does multinomial distribution mean? This page is about the various possible meanings of the acronym, abbreviation, shorthand or slang term: multinomial distribution.
Filter by:
Sort by:PopularityAlphabeticallyCategory
Term | Definition | Rating |
---|---|---|
MD | Multinomial Distribution statistics |
What does multinomial distribution mean?
- Multinomial distribution
- In probability theory, the multinomial distribution is a generalization of the binomial distribution. For example, it models the probability of counts for each side of a k-sided die rolled n times. For n independent trials each of which leads to a success for exactly one of k categories, with each category having a given fixed success probability, the multinomial distribution gives the probability of any particular combination of numbers of successes for the various categories. When k is 2 and n is 1, the multinomial distribution is the Bernoulli distribution. When k is 2 and n is bigger than 1, it is the binomial distribution. When k is bigger than 2 and n is 1, it is the categorical distribution. The Bernoulli distribution models the outcome of a single Bernoulli trial. In other words, it models whether flipping a (possibly biased) coin one time will result in either a success (obtaining a head) or failure (obtaining a tail). The binomial distribution generalizes this to the number of heads from performing n independent flips (Bernoulli trials) of the same coin. The multinomial distribution models the outcome of n experiments, where the outcome of each trial has a categorical distribution, such as rolling a k-sided dice n times. Let k be a fixed finite number. Mathematically, we have k possible mutually exclusive outcomes, with corresponding probabilities p1, ..., pk, and n independent trials. Since the k outcomes are mutually exclusive and one must occur we have pi ≥ 0 for i = 1, ..., k and ∑ i = 1 k p i = 1 {\displaystyle \sum _{i=1}^{k}p_{i}=1} . Then if the random variables Xi indicate the number of times outcome number i is observed over the n trials, the vector X = (X1, ..., Xk) follows a multinomial distribution with parameters n and p, where p = (p1, ..., pk). While the trials are independent, their outcomes X are dependent because they must be summed to n. In some fields such as natural language processing, categorical and multinomial distributions are synonymous and it is common to speak of a multinomial distribution when a categorical distribution is actually meant. This stems from the fact that it is sometimes convenient to express the outcome of a categorical distribution as a "1-of-K" vector (a vector with one element containing a 1 and all other elements containing a 0) rather than as an integer in the range 1 … K {\displaystyle 1\dots K} ; in this form, a categorical distribution is equivalent to a multinomial distribution over a single trial.
Know what is multinomial distribution? Got another good explanation for multinomial distribution? Don't keep it to yourself!
Still can't find the acronym definition you were looking for? Use our Power Search technology to look for more unique definitions from across the web!
Citation
Use the citation options below to add these abbreviations to your bibliography.
Style:MLAChicagoAPA
"multinomial distribution." Abbreviations.com. STANDS4 LLC, 2024. Web. 30 May 2024. <https://www.abbreviations.com/multinomial%20distribution>.
Discuss these multinomial distribution abbreviations with the community:
Report Comment
We're doing our best to make sure our content is useful, accurate and safe.
If by any chance you spot an inappropriate comment while navigating through our website please use this form to let us know, and we'll take care of it shortly.
Attachment
You need to be logged in to favorite.
Log In