A probability density function (PDF) is a function f(x) characterizing the probability distribution of a continuous random variable X. Its parameters are: (1) the support set S over which f(x) ≥ 0, (2) the normalization constraint ∫f(x)dx = 1 over S, and (3) the non-negative mapping f: ℝ → [0,∞) such that P(a ≤ X ≤ b) = ∫[a,b] f(x)dx. It persists through probability theory, statistical inference, and machine learning as the primary descriptor of continuous distributions, encoded in textbooks, software libraries, and computational practice. [formal: densitas probabilis | substrate: mind | horizon: a life | explicit: yes | epoch: 0.01]
Accepted ontology entry
probability density function
A probability density function (PDF) is a function f(x) characterizing the probability distribution of a continuous random variable X. Its parameters are: (1) the support set S over which f(x) ≥ 0, (2) the normalization constraint ∫f(x)dx…
Definition
Why it is in scope
A human-made mathematical construct in probability theory: a function describing the relative likelihood of a continuous random variable assuming a given value, such that the integral over any interval gives the probability of the variable falling within that interval. Built to persist through teaching, computation, and application in statistics and machine learning.
Names and aliases
- probability density functionen · CANONICAL
Relations from this entry
- cmsf6w1ek06ms3vv3snhiwxwlDEPENDS_ON →
PDF operationally depends on probability theory: it computes f(x) = dF/dx where F is the CDF, and integrates to probability P(a≤X≤b) = ∫f(x)dx. Remove probability theory's measure framework and the PDF ceases to function as a probability descriptor.
- cmsfj1tjj07d33vv3k8lgqtytDERIVED_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.
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Record identity
- Created
- Aug 5, 2026, 4:00 AM UTC
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- 059ba4e599009aece220353021f1566e3d8668742bc81a547701b8590f0019bd