The Rosenblatt transformation is an isoprobabilistic transformation
(refer to ) which is used under the following context :
is the input random vector, the
cumulative density functions of its components and its
copula, without no condition on its type.
Let us denote by a deterministic vector,
the limit state function of the
the event considered here and g(,) = 0 its boundary.
One way to evaluate the probability content of the event
is to use the Rosenblatt transformation which is a
diffeomorphism from into the standard space
, where distributions are normal, with zero mean, unit
variance and unit correlation matrix (which is equivalent in that
normal case to independent components).
Let us recall some definitions.
The cumulative distribution function of the
-dimensional random vector is
defined by its marginal distributions and the copula
through the relation: