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.
