Consider a mixed multi-normal distribution for which the density f(x; θ) can be expressed as where the πk are nonnegative quantities such that P k≥1 πk = 1, and fk(x; θ) is a multi-normal probability...

Consider a mixed multi-normal distribution for which the density f(x; θ) can be expressed as

where the πk are nonnegative quantities such that P k≥1 πk = 1, and fk(x; θ) is a multi-normal probability density function with mean vector θ and dispersion matrix Σk, k ≥ 1. Does this probability density function belong to the elliptically symmetric family?