The Double Pareto-Lognormal Distribution and its applications in actuarial science and finance
The purpose of this Master's thesis is to describe the double Pareto-lognormal distribution, show how the model can be extended by introducing explanatory variables in the model and present its large potential of applications in actuarial science and finance.  First, we give the definition of the double Pareto-lognormal distribution and present some of its properties based on the work of Reed and Jorgensen (2004). The parameters could be estimated by using the method of moments or maximum likelihood. Next, we add an explanatory variable to our model. The procedure of estimation for this model is also discussed. Finally, some numerical applications of our model are illustrated and some useful statistical tests are conducted.
Loi normale-Laplace Normal-Laplace distribution double Pareto-lognormal distribution maximum likelihood estimation Box-Cox transformation explanatory variables goodness-of-fit test