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PODrawing random values from a Fisher Distribution
 

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    <p>In my research, I am generating discrete planes that are intended to represent fractures in rock. The orientation of a fracture plane is specified by its dip and dip direction. Knowing this, I also know the components of the normal vector for each plane.</p> <p>So far, I have been drawing dip and dip direction independently from normal distributions. This is OK, but I would like to add the ability to draw from the Fisher distribution.</p> <p>The fisher distribution is described <a href="http://www.rocscience.com/downloads/swedge/webhelp/swedge/Fisher_Distribution.htm" rel="nofollow">HERE</a></p> <p><strong>Basically, I want to be able to specify an average dip and dip direction (or a mean vector) and a "fisher constant" or dispersion factor, k, and draw values randomly from that orientation distribution.</strong></p> <p>Additional Info: It seems like the "Von Mises-Fisher distribution" is either the same as what I've been calling the "Fisher distribution" or is somehow related. Some info on the Von Mises-Fisher distribution:</p> <p>As you can see, I've done some looking into this, but I admit that I don't fully understand the mathematics. I feel like I'm close, but am not quite getting it... Any help is much appreciated!</p> <p>If it helps, my programming is in FORTRAN.</p>
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    1. COMany questions on sampling are already on the site. Short short version: invert the CDF or reject. Existing questions: [Pseudorandom Number Generator - Exponential Distribution](http://stackoverflow.com/q/2106503) [Random number generator that produces a power-law distribution?](http://stackoverflow.com/q/918736) [Probability density function problem, from a paper, implemented using C++, not working as intended](http://stackoverflow.com/q/4103477) [How do I generate points that match a histogram?](http://stackoverflow.com/q/423006). Those aren't in Fortran, but the math is always the same.
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    2. COHave a look at these two references on directional data. Fisher, NI., Statistical Analysis of Circular Data, Cambridge University Press, 1993. ISBN 0-521-35018-2 Fisher, NI., Lewis, T., Embleton, BJJ. Statistical Analysis of Spherical Data, Cambridge University Press, 1993. ISBN 0-521-45699-1
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    3. COI guess one thing I don't understand: In the link that I provided, the distribution is in terms of theta. So basically the distribution is one dimensional, so I don't quite understand how it works in 3D? For example, I could simulate some value theta, but that would specify a ring around the mean vector, not an actual point.
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