A study about probabilistic and frequentist inferencial aspects of the generalized Student t distribution

• Grant number: 11/16158-7
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: December 01, 2011
• End date: November 30, 2012
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Statistics
• Principal Investigator: Caio Lucidius Naberezny Azevedo
• Grantee: Fernanda Ribeiro
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

The normal distribution (DN) predominated for a long time, the use of various methods of statistical analysis. Its various properties such as symmetry and forming a family closed for addition and conditioning make it very attractive, facilitating the development of such methods and the interpretation of results. Although the assumption of symmetry is found in many cases, the impossibility of accommodating outliers limits the use of DN. An alternative to the DN, which preserves the symmetry and can better accommodate the outliers is the Student t-distribution (DTS)). This distribution has tails heavier than the DN, this behavior is regulated by the degrees of freedom (df) parameter that characterizes this distribution. However, the decay rate of density t is always greater than the density of the DN (from zero to the points where the two densities intersect), the opposite was true after them. The generalized Student t distribution (DTSG), as the name suggests, is a generalization of the DTS as it considers a scaling parameter that provides additional properties. In addition to accommodating outliers, for example, the decay rate for tails in relation to density is controlled more flexibly by the second parameter. This velocity can be higher or lower than the DTS. Consequently, the DTSG can be used to model data sets in a larger number of situations that the DN and DTS. The objective of this project is to study in greater detail, inferential and probabilistic aspects often to the 3-parameter DTSG (DTSG3P), which corresponds to DTSG adding a location parameter, corresponding to the average.(AU)