Definition

Noun: A statistical distribution where all possible outcomes or values occur with exactly the same frequency or probability. It represents a state of perfect uniformity.

Usage

The term is used primarily in mathematics, statistics, and formal analysis to describe a perfectly uniform spread of data points, probabilities, or occurrences across a defined set.

Examples

• The researcher tested the random number generator for equidistribution of digits.
• In an ideal model, the dice exhibit equidistribution, with each face having a 1/6 probability.
• The theorem proves the equidistribution of the sequence across the interval.

Advanced Usage

• In Number Theory: Often used to describe sequences (like fractional parts of multiples of an irrational number) that become uniformly distributed in an interval.
  • The equidistribution of the sequence {nα} mod 1 is a classic result.
• In Computing: Refers to a property of pseudorandom number generators where outputs are spread evenly across the possible range.
  • A good hash function should aim for the equidistribution of keys.

Variants and Related Words

• Equidistributed (adjective): Describing something that has the property of equidistribution.
  • The points were equidistributed across the sampling space.
• Uniform Distribution (noun phrase): A common synonym in probability and statistics.

Synonyms

• Uniform distribution
• Rectangular distribution (in continuous probability)

Antonyms

• Skewed distribution
• Clustered distribution
• Uneven distribution

Noun

1. a flat distribution having equal frequencies of occurrence