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Moments of doubly truncated multivariate distributions

Grant number: 18/11580-1
Support type:Scholarships abroad - Research Internship - Doctorate
Effective date (Start): October 31, 2018
Effective date (End): October 30, 2019
Field of knowledge:Physical Sciences and Mathematics - Probability and Statistics
Principal Investigator:Larissa Avila Matos
Grantee:Christian Eduardo Galarza Morales
Supervisor abroad: Victor Hugo Lachos Davila
Home Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Local de pesquisa : University of Connecticut (UCONN), United States  
Associated to the scholarship:15/17110-9 - Robust estimation in spatial models for censored data, BP.DR

Abstract

Computation of the product moments of the truncated multivariate Student-t (TMVT) distribution under the double truncation have been presented by Lachos et al. (2017) (see also, Ho et al. (2012)). Following Lachos et al. (2017), this paper develops recurrence relations for integrals that involve the density of multivariate scale mixtures of skew-normal (SMSN) distributions. These recursions offer fast computation of arbitrary order product moments of truncated multivariate SMSN (TMVSMSN) and folded multivariate SMSN (FMVSMSN) distributions with the first two moments of the TMVSMSN and FMVSMSN as a byproduct. With these results, application to data containing bounded and missing responses is possible. The proposed methods will be implemented to a new R package (integrating C++ and Fortran), providing practitioners a convenient tool for further applications in several fields. (AU)