asymptotically independent events (english) - meaning, definition, translation, pronunciation

Part of Speech

"asymptotically independent events" is a noun phrase.

Phonetic Transcription

/ˌeɪsɪmpˈtɒtɪkli ˌɪndɪˈpɛndənt ɪˈvɛnts/

Meaning and Usage

"Asymptotically independent events" refers to a specific concept in probability theory and statistics where two or more events become independent as some parameter approaches a limit, typically infinity. In practical terms, it suggests that while events may exhibit some dependence for finite sizes or measurable values, their relationship may dissipate as the context extends towards larger scales or limits.

This term is generally used in academic and professional contexts, particularly in statistical research, theoretical computer science, and fields involving probabilistic modeling. It is less frequent in everyday conversation and more common in written, scientific literature.

Example Sentences

1. "In the large sample limit, the two random variables can be considered as asymptotically independent events."

2. В предельном случае с большим количеством выборок два случайных переменных могут рассматриваться как асимптотически независимые события.

3. "The researcher proved that the asymptotically independent events do not significantly correlate as the sample size increases."

4. Исследователь доказал, что асимптотически независимые события не коррелируют значительно по мере увеличения размера выборки.

5. "In statistical mechanics, certain processes are modeled as asymptotically independent events to simplify calculations."

6. В статистической механике некоторые процессы моделируются как асимптотически независимые события для упрощения расчетов.

Idiomatic Expressions

The phrase "asymptotically independent events" doesn't appear as part of established idiomatic expressions. However, the concept of independence and dependence can be explored through related terminologies and expressions in probability theory.

Example Sentences with Related Idiomatic Expressions

1. "When studying large datasets, it's often assumed that the variables behave as if they are asymptotically independent."

2. При изучении больших наборов данных часто предполагается, что переменные ведут себя так, как будто они асимптотически независимы.

3. "Statisticians often state that asymptotic independence simplifies many complex models."

4. Статистики часто утверждают, что асимптотическая независимость упрощает многие сложные модели.

5. "Researchers need to account for the fact that variables may not be asymptotically independent during small sample sizes."

6. Исследователям необходимо учитывать тот факт, что переменные могут быть не асимптотически независимыми при малых размерах выборки.

7. "The assumption of asymptotic independence can make analyses more tractable in high-dimensional spaces."

8. Предположение об асимптотической независимости может сделать анализ более управляемым в многомерных пространствах.

Etymology

The term "asymptotic" comes from the Greek word "asymptōtos," meaning "not falling together". In statistics, it relates to behavior as parameters approach a limit. The word "independent" originates from the Latin "independens," meaning "not dependent." When combined with "events," which comes from the Latin "eventus" (which refers to outcomes or occurrences), they create a specific terminology within statistical discourse.

Synonyms and Antonyms

Synonyms

• Approximately independent events
• Weakly independent events (in some contexts)

Antonyms

• Dependent events
• Correlated events

This comprehensive overview outlines the term "asymptotically independent events," its meanings, examples, idiomatic usage, etymology, synonyms, and antonyms, providing a solid grounding in its relevance to probability and statistics.