Phrase guide

Bernoulli distribution

noun · 2 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

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1

noun

Meaning 1

A discrete probability distribution that represents the result of a single trial, taking value 1 with "success" probability p and value 0 with "failure" probability q=1-p.

Definition source: English Wiktionary via Wiktextract

Topics: mathematics, sciences, statistics

Examples

  • 1977 [Wiley], Jean Dickinson Gibbons, Ingram Olkin, Milton Sobel, Selecting and Ordering Populations, 1999, Society for Industrial and Applied Mathematics, Unabridged corrected republication, page 103, Since both of these distributions involve the same parameter p, the problem under consideration here may be called either selection of the best Bernoulli distribution or selection of the best binomial distribution.
  • 2000, A. Berny, Selection and Reinforcement Learning for Combinatorial Optimization, Marc Schoenauer, Kalyanmoy Deb, Günther Rudolph, Xin Yao, Evelynne Lutton, Juan Julian Merelo, Hans-Paul Schwefel (editors), Parallel Problem Solving from Nature-PPSN VI, 6th International Conference Proceedings, Springer, page 601, In this paper however, we will only consider the family of Bernoulli distributions.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

2

noun

Meaning 2

a theoretical distribution of the number of successes in a finite set of independent trials with a constant probability of success

Definition source: Princeton WordNet 3.0

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: binomial distribution

Antonyms: none provided

Broader terms: distribution, statistical distribution

History

Etymology

After Swiss mathematician Jacob Bernoulli (1654—1705), one of many noted mathematicians of the Bernoulli family, who made important contributions to the field of probability.

Across languages

Translations

13 source translations are retained for this English entry.

  • Czech: alternativní rozdělení — distribution
  • Czech: Bernoulliho rozdělení — distribution
  • Finnish: Bernoullin jakauma — distribution
  • German: Bernoulli-Verteilung — distribution
  • Hungarian: Bernoulli-eloszlás — distribution
  • Icelandic: Bernoulli-dreifing — distribution
  • Icelandic: tvíliðudreifing — distribution
  • Icelandic: tvíkostadreifing — distribution
  • Polish: rozkład zero-jedynkowy — distribution
  • Polish: rozkład Bernoulliego — distribution
  • Portuguese: distribuição de Bernoulli — distribution
  • Romanian: distribuție Bernoulli — distribution
  • Russian: распределение Бернулли (raspredelenije Bernulli) — distribution