The Rocscience International Conference 2021 Proceedings are now available. Read Now

Search Results

Fisher Statistical Distribution

A Fisher Distribution is commonly used for modeling the distribution of 3-dimensional orientation vectors [Fisher (1953)], such as the distribution of joint orientations (pole vectors) on a sphere. A Fisher Distribution describes the angular distribution of orientations about a mean orientation vector, and is symmetric about the mean. The probability density function can be expressed as:

Fisher Distribution Equation Eqn.1

where is the angular deviation from the mean vector, in degrees, and Kis the "Fisher constant" or dispersion factor.

In UnWedge, a Fisher distribution can be used to define probabilistic joint orientation.

Fisher K

The Fisher K value describes the tightness or dispersion of an orientation cluster. A larger K value (e.g. 50) implies a tighter cluster, and a smaller K value (e.g. 20) implies a more dispersed cluster, as shown in the following figure.

Effect of Fisher K on a randomly generated joint set of 500 samples

Fisher K Values View

The Fisher K value can be estimated from Eqn. 2, for data sets with greater than approximately 30 vectors (poles) [Fisher (1953)].

Fisher K Value Equation Eqn.2

where N is the number of poles, and R is the magnitude of the resultant vector (i.e. the magnitude of the vector sum of all pole vectors in the set).

Standard Deviation

By analogy with a Normal distribution, it can be shown that the standard deviation of a Fisher distribution can be estimated from Eqn.3 [Butler (1992)].

Standard Deviation Equation Eqn.3

where is the "angular standard deviation" or "angular dispersion" of the Fisher Distribution, and K is the Fisher constant.

Account Icon - click here to log in or out of your account Shopping Cart icon Click here to search our site Click here to close Learning Tech Support Documentation Info Chevron Delete Back to Top View More" PDF File Calendar Location Language Fees Video Click here to visit Rocscience's LinkedIn page Click here to visit Rocscience's YouTube page Click here to visit Rocscience's Twitter page Click here to visit Rocscience's Facebook page Click here to visit Rocscience's Instagram page Bookmark Network Scroll down for more Checkmark Download Print Back to top Single User Multiple Users CPillar Dips EX3 RocFall RocPlane RocSupport RocTopple RS2 RS3 RSData RSPile Settle3 Slide2 Slide3 SWedge UnWedge Commercial License Education License Trial License Shop safe & secure Money-back guarantee