Normal-Laplace Distributions and their Applications
by Professor William J Reed
Abstract: In this talk I will introduce the normal-Laplace (NL) and the generalized normal-Laplace (GNL) distributions and discuss some of their applications. These include fitting size distributions; option pricing for financial assets; directional statistics and survival analysis.
The four-parameter NL distribution provides a good model for size distributions. It can also be used to provide a flexible family of hazard rate functions (including a 'bath-tub' shaped hazard) for use in survival analysis.
The five-parameter GNL distribution is used in the creation of a LÃ©vy process (Brownian-Laplace motion) whose increments can exhibit skewness and excess kurtosis (as seen in empirical logarithmic returns on stocks and other financial assets). An option pricing formula for assets following Brownian-Laplace motion is derived.
Finally wrapped versions of both the NL and GNL distributions provide attractive parametric models for directional data. They can exhibit both skewness and fat tails.
For More Information: Paul A. Pearce Email: P.Pearce@ms.unimelb.edu.au