Suppose that ϕ1,...,ϕk are k strict generator functions and define a new generator ϕ as a convex combination of these k generators, that is in which a1,...,ak are any non-negative constants which sum...

Suppose that ϕ1,...,ϕk are k strict generator functions and define a new generator ϕ as a convex combination of these k generators, that is

in which a1,...,ak are any non-negative constants which sum to 1. Show that ϕ(u) is a strict generator function. For the case in which k = 2, what is the corresponding copula function for ϕ(u)?