An empirical distribution is the frequency-based description of observed data values from a finite sample. It maps each distinct value (or bin of values) to its count or relative frequency within the observed dataset. Unlike a probability distribution, which specifies theoretical likelihoods, the empirical distribution is fully determined by the data at hand — it is the data summarized as a distribution. Formally, for a sample of n observations x₁, ..., xₙ, the empirical distribution assigns probability 1/n to each observation, forming a discrete distribution that converges to the true population distribution as n grows (Glivenko-Cantelli theorem). Its parameters are the sample values themselves; it persists through tabular frequency counts, cumulative frequency curves, and computational representations such as sorted observation arrays or histogram bins. [formal: distributio empirica | substrate: mind | horizon: a life | explicit: yes | epoch: 0.01]
Accepted ontology entry
empirical distribution
An empirical distribution is the frequency-based description of observed data values from a finite sample. It maps each distinct value (or bin of values) to its count or relative frequency within the observed dataset. Unlike a probability…
Definition
Why it is in scope
A statistical construct that represents the distribution of observed data values from a sample or experiment. It organizes actual measurements or observations into a frequency pattern, serving as the observable counterpart to theoretical probability distributions. Persisted through mathematical notation, statistical tables, and computational algorithms that summarize observed data.
Names and aliases
- empirical distributionen · CANONICAL
Relations from this entry
- cmsdard4403ny3vv3nkbt821lINSTANCE_OF →
TESTED INSTANCE_OF: an empirical distribution IS a specific kind of probability distribution — namely, the discrete distribution assigning equal probability (1/n) to each observed data point. A competent statistician would call an empirical distribution a probability distribution. Probability distribution is the nearest kind; no intermediate category exists between empirical distribution and probability distribution in standard statistical taxonomy.
- cmscvjayu038e3vv3k1h467mhDERIVED_FROM →
TESTED DERIVED_FROM: frequency distributions (tabular counts of observed values) predating the formal empirical distribution concept. The historical lineage goes from raw frequency tables → grouped frequency distributions → the formal empirical distribution (assigning 1/n probability to each observation). The formal concept derived from the earlier practice of tabulating frequencies.
- cmrvwajtn02ko2ceiy2wp3bp6DEPENDS_ON →
Present-tense necessity (Law 8b): the empirical distribution is a functional ON the sample — F_n(x) = (1/n)·Σ 1{X_i ≤ x} is defined over the sample values, and the entry's own carve says it 'describes observed data values from a finite sample.' Remove the sample now and the functional has no domain to operate on: there is nothing to describe, no F_n to compute — it stops OPERATING, it is not merely sayable. Not an ambient dependency (contrast: X DEPENDS_ON mathematics = STRIKE): the sample is the specific operational input, the same functional→input pattern as variance→probability-distribution and MLE→likelihood. (Note: the 'data' entry carves data CLEANING, so it is not the correct substrate; the carve's named input is the sample.)
Relations to this entry
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Record identity
- Created
- Aug 4, 2026, 3:13 AM UTC
- Content hash
- 8c0f1485bd14b2f00eeb3c5126d0436e50a46f223bb9d3bd22b206d947f86537