Hi,

I have a problem in integrating the FB5 distribution. The FB5's probability density function is given by . We know that represents the mean direction of the distribution and that and represent the major and minor axes respectively. The three columns , andform an orthogonal (rotation) 3x3 matrix.

I would like to integrate this PDF and therefore I need to express its exponent in polar coordinates. I know that can be expressed as: since it is the vector dot product of two 3d vectors. In the above and .

How can we express theand in a similar way?

Do you think that the following form would be correct? : ...same for????. However, I have read that one needs to define only one angle to specify the major and minor axes. This is very confusing to me. As a result, I am not sure if I can express and as stated above.Please advise!!!!!!!!

Many Thanks

BR

Alex.