Importance sampling with the generalized exponential power density

In this paper, the generalized exponential power (GEP) density is proposed as an importance function in Monte Carlo simulations in the context of estimation of posterior moments of a location parameter. This density is divided in five classes according to its tail behaviour which may be exponential, polynomial or logarithmic. The notion of p-credence is also defined to characterize and to order the tails of a large class of symmetric densities by comparing their tails to those of the GEP density. The choice of the GEP density as an importance function allows us to obtain reliable and effective results when p-credences of the prior and the likelihood are defined, even if there are conflicting sources of information. Characterization of the posterior tails using p-credence can be done. Hence, it is possible to choose parameters of the GEP density in order to have an importance function with slightly heavier tails than the posterior. Simulation of observations from the GEP density is also addressed.