Gamma Mixture: Bimodality, Inflexions and L-Moments

We study some characteristics of the mixture of two gamma distributions. Specifically, we characterize regions of the parameter space where the mixture density is bimodal and/or has four inflexion points and further, we provide formulae for the L-moments of such mixtures. These characteristics may be useful in density and parameter estimation methods, as well as in analytical and graphical modality testing procedures. With a simple example, we illustrate the estimation of the parameters of the gamma mixture by the method of L-moments. Such estimators are in some circumstances more efficient than those based on the conventional method of moments.