distribution function: meaning, definition, pronunciation and examples
C1Technical / Academic
Quick answer
What does “distribution function” mean?
A mathematical function that gives the probability that a random variable is less than or equal to a given value.
Audio
Pronunciation
Definition
Meaning and Definition
A mathematical function that gives the probability that a random variable is less than or equal to a given value.
In probability theory and statistics, the function that describes the likelihood of a random variable taking on a value less than or equal to a specific point. In logistics or general use, it can also refer to a function describing the allocation or dissemination of resources.
Dialectal Variation
British vs American Usage
Differences
No significant differences in meaning or usage. Spelling of related terms may differ (e.g., 'centre' vs. 'center' in 'distribution centre/center').
Connotations
Identically technical and neutral in both varieties.
Frequency
Equally frequent in academic and technical writing in both varieties.
Grammar
How to Use “distribution function” in a Sentence
The distribution function of [random variable] is...To compute/derive/find the distribution function for...A plot/graph of the distribution function shows...Vocabulary
Collocations
Examples
Examples of “distribution function” in a Sentence
verb
British English
- We need to distribution the samples.
American English
- We need to distribute the samples.
adverb
British English
- The data was distributed normally.
American English
- The data was distributed normally.
adjective
British English
- The distributional properties are key.
American English
- The distributional properties are key.
Usage
Meaning in Context
Business
Rare in general business; might be used in logistics modelling or quantitative analysis.
Academic
Core term in statistics, probability theory, econometrics, and quantitative sciences.
Everyday
Virtually never used in everyday conversation.
Technical
Fundamental term in mathematics, statistics, physics, engineering, and data science.
Vocabulary
Synonyms of “distribution function”
Strong
Neutral
Weak
Vocabulary
Antonyms of “distribution function”
Watch out
Common Mistakes When Using “distribution function”
- Confusing 'distribution function' (CDF) with 'probability density/mass function' (PDF/PMF). Using it without the necessary mathematical context, making meaning unclear. Incorrect pluralisation ('distributions functions').
FAQ
Frequently Asked Questions
No. The distribution function (CDF) gives cumulative probability (P(X ≤ x)). The density function (PDF) describes the relative likelihood at a point. The CDF is the integral of the PDF.
Primarily in mathematics, statistics, probability theory, econometrics, physics, engineering, and any field involving quantitative data analysis and stochastic modelling.
It is strongly technical. In business or logistics, people would use terms like 'distribution network', 'allocation system', or 'supply curve' instead. Using 'distribution function' outside maths/statistics is uncommon and may be misunderstood.
It is non-decreasing, right-continuous, and its limits are 0 at negative infinity and 1 at positive infinity.
A mathematical function that gives the probability that a random variable is less than or equal to a given value.
Distribution function is usually technical / academic in register.
Distribution function: in British English it is pronounced /ˌdɪs.trɪˈbjuː.ʃən ˌfʌŋk.ʃən/, and in American English it is pronounced /ˌdɪs.trəˈbjuː.ʃən ˌfʌŋk.ʃən/. Tap the audio buttons above to hear it.
Phrases
Idioms & Phrases
- “[No common idioms for this specific technical compound]”
Learning
Memory Aids
Mnemonic
Think of a CUMULATIVE 'DISTRIBUTION' of probabilities: The FUNCTION that stacks up all the probability up to a certain point.
Conceptual Metaphor
A GROWING PILE OF PROBABILITY. The function is imagined as accumulating likelihood like a pile of sand that grows taller as you move along the x-axis.
Practice
Quiz
What is the standard abbreviation for 'cumulative distribution function'?