< List of probability distributions < Directional distribution
A directional distribution measures spatial characteristics such as central tendency, dispersion and directional trends. These distributions can be applied to a wide variety of phenomena including reflected flux  neutrons , sea or wind waves , highway traffic  and spatial fibre processes .
In ArcGIS and other spatial statistics tools, it measures whether a distribution of geographic features shows a directional trend.
The directional distribution function
The directional distribution function (also called the spreading function, the angular distribution function or directional spreading function) is a function that represents the directional distribution of wave energy. It is dimensionless and varies with frequency . “Dimensionless” means that the function does not have any units of measurement.
It is part of the process of estimating frequency-direction spectra. The frequency-direction spectrum (also called the directional spectrum or wave spectrum) represents the distribution of wave energy in terms of frequency and direction. It is a two-dimensional function, with frequency on the x-axis and direction on the y-axis.
A directional distribution function D(fn, θm) and its frequency-direction spectrum S(fn, θm) are related in the following way :
- f = frequency
- θm = a discrete angle showing wave energy arrival direction (counterclockwise from true north) with values from θ1 = -180 degrees to θ181=180 degrees in steps of dθ = 2 degrees.
- m = a direction index with values m=1 to m=M=181.
- S(fn) = sea surface displacement variance spectral density.
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 Pyshkina, M. et al. (2021). Study of neutron energy and directional distribution at the Beloyarsk NPP selected workplaces. Nuclear Engineering and Technology Volume 53, Issue 5, May 2021, Pages 1723-1729
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