A cumulative distribution function (CDF) is a mathematical function F(x) that maps each real value x to the probability P(X ≤ x) that a random variable X takes a value at or below x. Its parameters are: (1) a real-valued random variable X with a defined sample space, (2) the cumulative probability function F(x) = P(X ≤ x). It persists as a mathematical construct encoded in notation, computation, and teaching. [formal: distributio cumulativa | substrate: mind | horizon: as-long-as-us | explicit: yes | epoch: 0.01]
Accepted ontology entry
cumulative distribution function
A cumulative distribution function (CDF) is a mathematical function F(x) that maps each real value x to the probability P(X ≤ x) that a random variable X takes a value at or below x. Its parameters are: (1) a real-valued random variable X…
Definition
Why it is in scope
A human-made mathematical function that gives the probability that a real-valued random variable takes a value less than or equal to x — the integral of the probability density function, used to characterize the distribution of random variables
Names and aliases
- cumulative distribution functionen · CANONICAL
Relations from this entry
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The CDF's operation is to compute P(X ≤ x) for every x — this requires probability measures, cumulative probability, and the axiomatic framework of probability theory. Remove probability theory and the CDF ceases to operate: there is no notion of P(X ≤ x) without it. The which-came-first test confirms: probability theory (Kolmogorov 1933, and intuitively much older) predates the CDF formalism.
Relations to this entry
- cmsfk7mne07ey3vv30jp9f3r6← DERIVED_FROM
PDF is built on the CDF concept: historically the distribution function (CDF) was the primary way to describe probability distributions. PDF arises when you add the differentiability assumption — it is the derivative of the CDF. CDF existed first and fed into PDF.
- cmsdh2muw03x63vv3ygonn3td← INSTANCE_OF
ECDF IS a specific kind of cumulative distribution function, estimating the CDF from observed data rather than assuming a theoretical distribution. The ECDF is a concrete instance of the general CDF concept. Tested: CDF is older/more foundational.
- cmsk3skhy03w2nobp23sljvfr← DERIVED_FROM
ECDF plot is derived from the cumulative distribution function concept — it plots the empirical CDF of data. The CDF existed first and fed into the creation of ECDF plots.
Record identity
- Created
- Aug 5, 2026, 3:28 AM UTC
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- 6a0fd676b42bf52b656a5f309b80e99bb5bb3bac353073914864868a87db9299