  Diurnal temperature range is an important variable in climate science that
can provide information regarding climate variability and climate change.
Changes in diurnal temperature range can have implications for hydrology, human
health and ecology, among others. Yet, the statistical literature on modelling
diurnal temperature range is lacking. In this paper we propose to model the
distribution of diurnal temperature range using the five-parameter lambda (FPL)
distribution. Additionally, in order to model diurnal temperature range with
explanatory variables, we propose a distributional quantile regression model
that combines quantile regression with marginal modelling using the FPL
distribution. Inference is performed using the method of quantiles. The models
are fitted to 30 years of daily observations of diurnal temperature range from
112 weather stations in the southern part of Norway. The flexible FPL
distribution shows great promise as a model for diurnal temperature range, and
performs well against competing models. The distributional quantile regression
model is fitted to diurnal temperature range data using geographic, orographic
and climatological explanatory variables. It performs well and captures much of
the spatial variation in the distribution of diurnal temperature range in
Norway.
