Studying properties of a random variable in dual domains
- Day - Time: 10 February 2015, h.11:00
- Place: Area della Ricerca CNR di Pisa - Room: C-40
- Junying Zhang (Xidian University, Dept of Computer Science, Xidian, China)
Studying fundamental properties of a random variable is a key step towards its applications. Here we provide a paradigm of study in density domain, in characteristic domain and transfer between the domains, where density domain study is based on probability density function (pdf) and characteristic study is based on characteristic function amplitude (cfa) of the variable.
Novel quantities are introduced: dentropy and centropy. The maximum entropy principle with unknowns embraced in constraints finds brilliant comings when applied to either domain with the quantities: stable/GGD variable is the maximum dentropy/centropy solution. Based on the results, stable and GGD reference of a variable are defined and non-stability and non-GGD measure are presented.
Property duality is found for variables with a same representation form for one in density domain and for another in characteristic domain. The dualities are on statistics, references, measures, projections/directions, mixture models and so forth. This makes it promising to study a variable from its dual. The paradigm stipulates a new kind of language in probability theory and practice for insights of a variable.