Moment estimates foe mixtures of sevebal distributions with different means or scales
Christopher Stroude Withers · Communication in Statistics- Theory and Methods · 1996
Mixtures of c distributions with (I) different means θ = (θ′,…,θc) and common scale λ or (11) different scales θ′ and common mean λ or (111) each distribution being gamma with different parameters θ but common scale, are particular cases of mixtures where the unknown parameters θ,λ and the unknown mixture probabilities p′ = (p1,…,pc) can be expressed in various ways as functions of 2c or more moments. We consider three such families of distributions. Replacing moments by sample moments yields asymptotically normal estimates for p,θ and λ. The method is illustrated with rainfall data.