The problem I am facing can be described like this: I have two matrices, as an example, let's assume two sample velocity data which were obtained from bottom of a lake at an instance t:
Stream-wise velocity, A = \begin{bmatrix}3&3.1&3.2&3.11\\2&2.5&2.58&2.69\\0.1&0.12&0.1&0.15\end{bmatrix}
and
Upward velocity, B = \begin{bmatrix}0.4&0.5&0.3&0.1\\0.35&0.2&0.5&0.8\\0.05&0.01&0.05&0.01\end{bmatrix}
their measurement location is defined using X and Y matrix.
Stream-wise position, X = \begin{bmatrix}1&2&3&4\\1&2&3&4\\1&2&3&4\end{bmatrix}
and
Upward position, Y = \begin{bmatrix}3&3&3&3\\2&2&2&2\\1&1&1&1\end{bmatrix}
So, the co-ordinate system is located at the bottom of the lake.
Here's my question: How can I calculate Joint PDF for A & B in this case? Please describe the process of calculation in details. Thanks in advance.