Birnbaum–Saunders spatial modelling and diagnostics applied to agricultural engineering data

  • Fabiana Garcia-Papani
  • Miguel Angel Uribe-Opazo
  • Victor Leiva
  • Robert G. Aykroyd
Original Paper


Applications of statistical models to describe spatial dependence in geo-referenced data are widespread across many disciplines including the environmental sciences. Most of these applications assume that the data follow a Gaussian distribution. However, in many of them the normality assumption, and even a more general assumption of symmetry, are not appropriate. In non-spatial applications, where the data are uni-modal and positively skewed, the Birnbaum–Saunders (BS) distribution has excelled. This paper proposes a spatial log-linear model based on the BS distribution. Model parameters are estimated using the maximum likelihood method. Local influence diagnostics are derived to assess the sensitivity of the estimators to perturbations in the response variable. As illustration, the proposed model and its diagnostics are used to analyse a real-world agricultural data set, where the spatial variability of phosphorus concentration in the soil is considered—which is extremely important for agricultural management.


Asymmetric distributions Local influence Matérn model Maximum likelihood methods Monte Carlo simulation Non-normality R software Spatial data analysis 



The authors thank the Editors and anonymous referees for their constructive comments on an earlier version of the manuscript, which resulted in this improved version. We are grateful to Carolina Brianezi-Melchior, who translated this work into English, from its original Portuguese. This research work was partially supported by CNPq Grants from the Brazilian Government, and by FONDECYT 1120879 Grant from the Chilean Government.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Fabiana Garcia-Papani
    • 1
  • Miguel Angel Uribe-Opazo
    • 1
  • Victor Leiva
    • 2
  • Robert G. Aykroyd
    • 3
  1. 1.Postgraduate Program in Agricultural Engineering, Centre of Exact Sciences and TechnologyUniversidade Estadual do Oeste do ParanáCascavelBrazil
  2. 2.Faculty of Engineering and SciencesUniversidad Adolfo IbáñezViña del MarChile
  3. 3.Department of StatisticsUniversity of LeedsLeedsUK

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