There are seven families of isogonal each family having a real-valued parameter determining the overlap between sides of adjacent tiles or the ratio between the edge lengths of different tiles.
12.
Note that, as in the above case of a scalar-valued parameter, the function A ( \ boldsymbol \ theta ) or equivalently g ( \ boldsymbol \ theta ) is automatically determined once the other functions have been chosen, so that the entire distribution is normalized.
13.
VP2 supports the same data types and data processing operations as VP1, but has additional features for better support of high level languages such as demarcation of subroutines, by-value parameters, and a very large theoretical maximum number of registers local to the subroutine for use as local variables.
14.
"' McCullagh's parametrization "', introduced by Peter McCullagh, professor of statistics at the University of Chicago uses the two parameters of the non-standardised distribution to form a single complex-valued parameter, specifically, the complex number ? = ? + " i " ?, where " i " is the imaginary unit.
15.
If all parameters are scalar values, then this means that there will be one more hyperparameter than parameter; but this also applies to vector-valued and matrix-valued parameters . ( See the general article on the exponential family, and consider also the Wishart distribution, conjugate prior of the covariance matrix of a multivariate normal distribution, for an example where a large dimensionality is involved .)
