Multivariate Statistics Beyond Normality

Multivariate Statistics Beyond Normality is a unique book that provides a modern and original introduction to multivariate statistics and then extends it beyond the multivariate normal distribution. Specifically, the extensions include spherical and elliptical distributions, the skew-normal distributions and related distributions, a detailed treatment of unified skew-elliptical distributions and their sub-models, a study of weighted and selection multivariate distributions, and over 100 illustrative examples. Written by two leading specialists on multivariate statistics, this book includes the most recent and some novel results on skew-normal and related distributions, covering both singular and nonsingular cases in a unified way, and contains unpublished results on elliptical distributions from the first author's Ph.D. thesis. It presents illustrative data applications beyond normality that are relevant to both classical frequentist inference and Bayesian analysis. Designed for a broad readership by starting from basic fundamental concepts and leading to more advanced topics, the book includes 150 exercises, many original, to practice the concepts presented across the chapters, as well as 40 open problems that still need to be further researched.

Key Features

• Provides a modern and original introduction to multivariate statistics
• Extends classical results beyond normality
• Includes over 100 illustrative examples, 100 exercises, and 40 open research problems
• Uses color-coded highlights to facilitate learning
• Promotes both frequentist statistics and Bayesian analysis

Reinaldo B. Arellano-Valle is a Professor of Statistics at the Pontificia Universidad Católica de Chile (PUC) in Santiago, Chile. He received his Ph.D. in Statistics in 1994 from the University of Sao Paulo, Brazil. He is an international leader in the field of multivariate statistics, an elected member of the International Statistical Institute (ISI), and has received the 2019 Mahalanobis Award from the ISI for outstanding research in multivariate statistics.

Marc G. Genton is the Al-Khawarizmi Distinguished Professor of Statistics at the King Abdullah University of Science and Technology (KAUST) in Saudi Arabia. He received his Ph.D. degree in Statistics in 1996 from the Swiss Federal Institute of Technology (EPFL), Lausanne. He is a fellow of the American Statistical Association (ASA), of the Institute of Mathematical Statistics (IMS), and the American Association for the Advancement of Science (AAAS), an elected member of the International Statistical Institute (ISI), and he has received multiple awards.