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

Fabiana Garcia-Papani, Miguel Angel Uribe-Opazo, VICTOR ELISEO LEIVA SANCHEZ, Robert G. Aykroyd

Research output: Contribution to journalArticlepeer-review

42 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)105-124
Number of pages20
JournalStochastic Environmental Research and Risk Assessment
Volume31
Issue number1
DOIs
StatePublished - 1 Jan 2017

Keywords

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

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