Applications of The Normal Laplace and Generalized Normal Laplace Distributions

Two parametric models for income and financial return distributions are presented. There are the four-parameter normal Laplace (NL) and the five-parameter generalized normal Laplace (GNL) distributions. Their properties are discussed; furthermore, estimation of the parameters by the method of moments and maximum likelihood is presented. The performances of fitting the two models to nine empirical distributions of family income have been evaluated and compared against the fourand five-parameter generalized beta2 (GB2) and generalized beta (GB) distributions which had been previously claimed as best-fitting fourand fiveparameter models for income distribution. The results demonstrate that the NL distribution has better performance than the GB and GB2 distributions with the GNL distribution providing an even better fit. Limited application to data on financial log returns shows that the fit of the GNL is comparable to the well-known generalized hyperbolic distribution. However, the GNL suffers from a lack of closed-form expressions for its probability density and cumulative distribution functions, and fitting the distribution numerically is slow and not always reliable. The results of this thesis suggest a strong case for considering the GNL family as parametric models for income data and possibly for financial logarithmic returns.