A class of rectangle-screened multivariate normal distributions and its applications

Abstract

A screening problem is tackled by proposing a parametric class of distributions designed to match the behavior of the partially observed screened data. This class is obtained from the nontruncated marginal of the rectangle-truncated multivariate normal distributions. Motivations for the screened distribution as well as some of the basic properties, such as its characteristic function, are presented. These allow us a detailed exploration of other important properties that include closure property in linear transformation, in marginal and conditional operations, and in a mixture operation as well as the first two moments and some sampling distributions. Various applications of these results to the statistical modelling and data analysis are also provided.

Keywords:

• truncated multivariate normal distribution
• rectangle-screened multivariate distribution
• closure property
• applications

AMS 2000 Subject Classifications:

• 62E10
• 62F30

Acknowledgements

The first author's research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (2013R1A2A2A01004790). This work is supported by the research program of Dongguk University. The corresponding author's research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education, Science and Technology (2013R1A1A2005995).