Dyadic distribution
Encyclopedia
A dyadic distribution is a specific type of discrete or categorical probability distribution
that is of some theoretical importance in data compression
.
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
.
Probability distribution
In probability theory, a probability mass, probability density, or probability distribution is a function that describes the probability of a random variable taking certain values....
that is of some theoretical importance in data compression
Data compression
In computer science and information theory, data compression, source coding or bit-rate reduction is the process of encoding information using fewer bits than the original representation would use....
.
Definition
A dyadic distribution on the nonnegative integers 0, 1, 2, ... is a probability distributionProbability distribution
In probability theory, a probability mass, probability density, or probability distribution is a function that describes the probability of a random variable taking certain values....
whose probability mass function
Probability mass function
In probability theory and statistics, a probability mass function is a function that gives the probability that a discrete random variable is exactly equal to some value...
is
where nu is some (positive) integer
Integer
The integers are formed by the natural numbers together with the negatives of the non-zero natural numbers .They are known as Positive and Negative Integers respectively...
. More generally it is a categorical distribution
Categorical distribution
In probability theory and statistics, a categorical distribution is a probability distribution that describes the result of a random event that can take on one of K possible outcomes, with the probability of each outcome separately specified...
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
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...
.