Dyadic distribution

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Revision as of 05:23, 27 August 2023 by imported>Tgianit (Categorical distributions have finite support. Cover & Thomas say [pg. 132] that a PMF is dyadic if log (1/p(x)) is an integer for all x, with no constraint that the support need be finite.)

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A dyadic (or 2-adic) distribution is a specific type of discrete probability distribution that is of some theoretical importance in data compression.

Definition

A dyadic distribution is a probability distribution whose probability mass function is

f (i) = 2^{- x_{i}}

where $x_{i}$ is some whole number.

It is possible to find a binary code defined on this distribution, which has an average code length that is equal to the entropy.^[1]

References

Template:Reflist

Cover, T.M., Joy A. Thomas, J.A. (2006) Elements of information theory, Wiley. Template:ISBN

Template:ProbDistributions

↑ Cover, T.M., Joy A. Thomas, J.A. (2006) Elements of information theory, Wiley. Template:ISBN

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