Abstract
This chapter provides the statistical background and analytical tools used throughout the remainder of this book. Topics include a description of stochastic hydrology and simulations of drought statistics, regression methods that build from simple linear regression to more complex approaches, a detailed discussion of goodness of fit, an overview of temporal trend analysis and a review of methods that link spatial and temporal patterns of drought. Each section highlights the assumptions and limitations of their respective approaches, while also providing suggestions for research examples and extensions related to characterising hydrologic drought. Worked examples using the included data are provided to demonstrate each approach and interpretation of their results. The chapter concludes with a brief description of some novel promising analytical techniques.