Following McNeil and Nešlehová (2009), we present some weaker conditions under which a partially nested Archimedean copula with arbitrary nesting levels is still a copula. Relaxing the conditions on the generators enable researchers to model data sets more efficiently.

Nested Archimedean copulas recently gained interest since they generalize the well-known class of Archimedean copulas to allow for partial asymmetry. Sampling algorithms and strategies have been well investigated for nested Archimedean copulas. However, for likelihood based inference it is...