< 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 [1] neutrons [2], sea or wind waves [3], highway traffic [4] and spatial fibre processes [5].

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 [3]. “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(f _{n}, θ_{m})* and its frequency-direction spectrum

*S(f*are related in the following way [6]:

_{n}, θ_{m})Where:

*f*= frequency*θ*= a discrete angle showing wave energy arrival direction (counterclockwise from true north) with values from_{m}*θ*= -180 degrees to_{1}*θ*=180 degrees in steps of d_{181}*θ*= 2 degrees.*m*= a direction index with values*m*=1 to*m*=*M*=181.*S(f*= sea surface displacement variance spectral density._{n})

## References

[1] NBS Technical Note, Vol. 439. 1968. U.S. Department of Commerce, National Bureau of Standards.

[2] 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

[3] Goda, Y. (2000). Random Seas and Design of Maritime Structures. World Scientific.

[4] Sharma, S. & Singh. A. (1992). Reexamination of Directional Distribution of Highway Traffic. Journal of Transportation Engineering. Vol. 118, Issue 2.

[5] Mattfeldt, T. et al. (1994). Estimation of the directional distribution of spatial fibre processes using stereology and confocal scanning laser microscopy. Journal of Microscopy, Vol 173, Issue 2, p. 87-101.

[6] Long, C. (1995). Directional Wind Wave Characteristics at Harvest Platform. U.S. Army Engineer Waterways Experiment Station.

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