A dyadic (or 2-adic) distribution is a specific type of discrete or categorical probability distribution that is of some theoretical importance in data compression.
Definition
A dyadic distribution is a probability distribution whose probability mass function is
\( {\displaystyle f(n)=2^{-n},\quad n\in N} \)
where n 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]
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References
Cover, T.M., Joy A. Thomas, J.A. (2006) Elements of information theory, Wiley. ISBN 0-471-24195-4
Probability distributions (List)
Discrete univariate
with finite support
Benford Bernoulli beta-binomial binomial categorical hypergeometric Poisson binomial Rademacher soliton discrete uniform Zipf Zipf–Mandelbrot
Discrete univariate
with infinite support
beta negative binomial Borel Conway–Maxwell–Poisson discrete phase-type Delaporte extended negative binomial Flory–Schulz Gauss–Kuzmin geometric logarithmic negative binomial parabolic fractal Poisson Skellam Yule–Simon zeta
Continuous univariate
supported on a bounded interval
arcsine ARGUS Balding–Nichols Bates beta beta rectangular continuous Bernoulli Irwin–Hall Kumaraswamy logit-normal noncentral beta raised cosine reciprocal triangular U-quadratic uniform Wigner semicircle
Continuous univariate
supported on a semi-infinite interval
Benini Benktander 1st kind Benktander 2nd kind beta prime Burr chi-squared chi Dagum Davis exponential-logarithmic Erlang exponential F folded normal Fréchet gamma gamma/Gompertz generalized gamma generalized inverse Gaussian Gompertz half-logistic half-normal Hotelling's T-squared hyper-Erlang hyperexponential hypoexponential inverse chi-squared
scaled inverse chi-squared inverse Gaussian inverse gamma Kolmogorov Lévy log-Cauchy log-Laplace log-logistic log-normal Lomax matrix-exponential Maxwell–Boltzmann Maxwell–Jüttner Mittag-Leffler Nakagami noncentral chi-squared noncentral F Pareto phase-type poly-Weibull Rayleigh relativistic Breit–Wigner Rice shifted Gompertz truncated normal type-2 Gumbel Weibull
discrete Weibull Wilks's lambda
Continuous univariate
supported on the whole real line
Cauchy exponential power Fisher's z Gaussian q generalized normal generalized hyperbolic geometric stable Gumbel Holtsmark hyperbolic secant Johnson's SU Landau Laplace asymmetric Laplace logistic noncentral t normal (Gaussian) normal-inverse Gaussian skew normal slash stable Student's t type-1 Gumbel Tracy–Widom variance-gamma Voigt
Continuous univariate
with support whose type varies
generalized chi-squared generalized extreme value generalized Pareto Marchenko–Pastur q-exponential q-Gaussian q-Weibull shifted log-logistic Tukey lambda
Mixed continuous-discrete univariate
rectified Gaussian
Multivariate (joint)
Discrete
Ewens
multinomial
Dirichlet-multinomial
negative multinomial
Continuous
Dirichlet
generalized Dirichlet
multivariate Laplace
multivariate normal
multivariate stable
multivariate t
normal-inverse-gamma
normal-gamma
Matrix-valued
inverse matrix gamma
inverse-Wishart
matrix normal
matrix t
matrix gamma
normal-inverse-Wishart
normal-Wishart
Wishart
Directional
Univariate (circular) directional
Circular uniform
univariate von Mises
wrapped normal
wrapped Cauchy
wrapped exponential
wrapped asymmetric Laplace
wrapped Lévy
Bivariate (spherical)
Kent
Bivariate (toroidal)
bivariate von Mises
Multivariate
von Mises–Fisher
Bingham
Degenerate and singular
Degenerate
Dirac delta function
Singular
Cantor
Families
Circular compound Poisson elliptical exponential natural exponential location–scale maximum entropy mixture Pearson Tweedie wrapped
Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
Hellenica World - Scientific Library
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