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A '''dyadic distribution''' is a specific type of discrete or categorical [[probability distribution]] that is of some theoretical importance in [[data compression]]. | |||
==Definition== | |||
A dyadic distribution on the nonnegative integers 0, 1, 2, ... is a [[probability distribution]] whose [[probability mass function]] is | |||
:<math>f(u) = 2^{-n_u},\quad u \in U</math> | |||
where ''n''<sub>''u''</sub> is some (positive) [[integer]]. More generally it is a [[categorical distribution]] in which the probability assigned to any label is of the above form | |||
It is possible to find a code defined on this distribution, which has an average code length that is equal to the [[entropy]].{{Citation needed|date=August 2010}} | |||
{{No footnotes|date=July 2010}} | |||
==References== | |||
*Cover, T.M., Joy A. Thomas, J.A. (2006) ''Elements of information theory'', Wiley. ISBN 0-471-24195-4 | |||
{{ProbDistributions|discrete-infinite}} | |||
{{DEFAULTSORT:Dyadic Distribution}} | |||
[[Category:Types of probability distributions]] | |||
[[Category:Data compression]] | |||
[[Category:Discrete distributions]] | |||
[[Category:Probability distributions]] | |||
Latest revision as of 02:27, 23 March 2013
A dyadic distribution is a specific type of discrete or categorical probability distribution that is of some theoretical importance in data compression.
Definition
A dyadic distribution on the nonnegative integers 0, 1, 2, ... is a probability distribution whose probability mass function is
where nu is some (positive) integer. More generally it is a categorical distribution in which the probability assigned to any label is of the above form
It is possible to find a code defined on this distribution, which has an average code length that is equal to the entropy.Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park.
References
- Cover, T.M., Joy A. Thomas, J.A. (2006) Elements of information theory, Wiley. ISBN 0-471-24195-4
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