cumulative distribution function: meaning, definition, pronunciation and examples
Very LowTechnical/Scientific
Quick answer
What does “cumulative distribution function” mean?
In probability theory and statistics, a function that gives the probability that a random variable is less than or equal to a certain value.
Audio
Pronunciation
Definition
Meaning and Definition
In probability theory and statistics, a function that gives the probability that a random variable is less than or equal to a certain value.
A fundamental concept describing how probabilities accumulate across the range of possible outcomes for a variable, often visualized as an S-shaped curve.
Dialectal Variation
British vs American Usage
Differences
No significant differences in meaning or usage between UK and US academic/technical contexts.
Connotations
Purely technical, neutral connotation in both varieties.
Frequency
Used with identical frequency in statistical literature worldwide.
Grammar
How to Use “cumulative distribution function” in a Sentence
The CDF of XF(x) is the cumulative distribution functionto compute the cumulative distribution function forVocabulary
Collocations
Examples
Examples of “cumulative distribution function” in a Sentence
verb
British English
- N/A
American English
- N/A
adverb
British English
- N/A
American English
- N/A
adjective
British English
- N/A
American English
- N/A
Usage
Meaning in Context
Business
Virtually never used outside of specialised risk analysis or quantitative finance roles.
Academic
Core terminology in statistics, probability theory, econometrics, and engineering courses.
Everyday
Not used.
Technical
Essential in data science, statistical modelling, signal processing, and reliability engineering.
Vocabulary
Synonyms of “cumulative distribution function”
Strong
Neutral
Weak
Vocabulary
Antonyms of “cumulative distribution function”
Watch out
Common Mistakes When Using “cumulative distribution function”
- Confusing CDF with PDF (Probability Density Function).
- Saying 'cumulative density function' (incorrect blend).
- Using it as a countable plural (e.g., 'different cumulative distribution functions').
FAQ
Frequently Asked Questions
No. The CDF gives cumulative probability (area under the PDF curve to the left of a point), while the PDF gives the density (the 'height' of the curve at a point). For continuous variables, the CDF is the integral of the PDF.
A CDF always takes values between 0 and 1 inclusive, as it represents probability. It starts at 0 (or a very low limit) and increases to 1.
No, a proper CDF is a non-decreasing function. As x increases, the accumulated probability cannot go down.
Many statistical tests, like the Kolmogorov-Smirnov test, compare empirical CDFs to theoretical ones to assess how well data fits a distribution.
In probability theory and statistics, a function that gives the probability that a random variable is less than or equal to a certain value.
Cumulative distribution function is usually technical/scientific in register.
Cumulative distribution function: in British English it is pronounced /ˈkjuːmjʊlətɪv dɪstrɪˈbjuːʃən ˈfʌŋkʃən/, and in American English it is pronounced /ˈkjuːmjəleɪtɪv dɪstrɪˈbjuːʃən ˈfʌŋkʃən/. Tap the audio buttons above to hear it.
Phrases
Idioms & Phrases
- “N/A”
Learning
Memory Aids
Mnemonic
CDF: Counts Data cumulatively For any point x, it tells you the Fraction of data less than or equal to x.
Conceptual Metaphor
A running total of likelihood; a measuring cup filling with probability as you move along the number line.
Practice
Quiz
What does the value of a cumulative distribution function F(x) represent?