Heterogeneity and Multivariate Logistic Distributions

Abstract

Heterogeneity of populations, sets of objects, supply, or demand in statistical models often is ignored or described outside and prior to statistical model analysis such that this analysis runs for fictitious independent and mean objects or on an aggregate level. The reasons are lack or complexity of appropriate models incorporating heterogeneity and comfortable results for i.i.d. variables from sampling theory. Complete heterogeneity has to include and describe two essential aspects (1) different individual behavior and (2) dependence of this behavior. For aspect (1) convolution and compounding of sufficiently flexible distributions are well-established techniques. With respect to univariate logistic distributions these techniques were used since Dubey (1969) to produce many satisfying results (Knüppel 1986). For aspect (2) multivariate extensions are self-suggesting.