A functional approach to distribution modelling : the spliced generalised normal distribution

Abstract

A new body and tail generalisation of the normal distribution is introduced, the spliced generalised normal (SGN). A special case of the SGN, the tail-adjusted normal distribution, is further generalised with two-piece scaling to accommodate di erent combinations of skewness and tail weight in data. The two-piece scaled tail-adjusted normal (TPTAN) is thoroughly studied with the derivations of various statistical properties such as the probability density function, cumulative distribution function, quantile function, moments, and Fischer information. The applicability of the SGN distribution is demonstrated by the application of the TPTAN to light and heavy-tailed data sets. The small and large sample performance of the TPTAN is investigated with an extensive simulation study. The methods of estimation include maximum likelihood and Kolmogorov-Smirnov estimation. The goodness of t is evaluated by likelihood criteria and hypothesis tests such as Akaike information criterion, Bayesian information criterion, consistent Akaike information criterion, Hannan-Quinn information criterion, and the KS and Bayes factor tests.