Kriging with external drift in a Birnbaum-Saunders geostatistical model

Spatial models to describe dependent georeferenced data are applied in different fields and, particularly, are used to analyze earth and environmental data. Most of these applications are carried out under Gaussian spatial models. The Birnbaum-Saunders distribution is a unimodal and positively skewed model which has received considerable attention in several areas, including earth and environmental sciences. In addition, theoretical arguments have been provided to justify its usage in the data modeling from these sciences, at least in the same settings where the lognormal distribution can be employed. This paper presents kriging with external drift based on a Birnbaum-Saunders spatial model. The maximum likelihood method is considered to estimate its parameters. The results obtained in the paper are illustrated by an experimental data set related to agricultural management. Specifically, in this illustration, the spatial variability of magnesium content in the soil as a function of calcium content is analyzed.