A method to obtain new copulas from a given one

Given a strictly increasing continuous function φ from [0, 1] to [0, 1] and its pseudo-inverse φ <Superscript>[−1]</Superscript>, conditions that φ must satisfy for C<Subscript> φ </Subscript>(x<Subscript>1</Subscript>, . . . ,x<Subscript>n</Subscript>)=φ <Superscript>[−1]</Superscript>(C(φ(x<Subscript>1</Subscript>), . . . ,φ(x<Subscript>n</Subscript>))) to be a copula for any copula C are studied. Some basic properties of the copulas obtained in this way are analyzed and several examples of generator functions φ that can be used to construct copulas C<Subscript> φ </Subscript> are presented. In this manner, a method to obtain from a given copula C a variety of new copulas is provided. This method generalizes that used to construct Archimedean copulas in which the original copula C is the product copula, and it is related with mixtures Copyright Springer-Verlag 2005