Abstract:
Natural hazards (events that may cause actual disasters) are established in the literature as
major causes of various massive and destructive problems worldwide. The occurrences of
earthquakes, floods and heat waves affect millions of people through several impacts. These
include cases of hospitalisation, loss of lives and economic challenges. The focus of this study
was on the risk reduction of the disasters that occur because of extremely high temperatures
and heat waves. Modelling average maximum daily temperature (AMDT) guards against the
disaster risk and may also help countries towards preparing for extreme heat. This study
discusses the use of the r largest order statistics approach of extreme value theory towards
modelling AMDT over the period of 11 years, that is, 2000–2010. A generalised extreme value
distribution for r largest order statistics is fitted to the annual maxima. This is performed in
an effort to study the behaviour of the r largest order statistics. The method of maximum
likelihood is used in estimating the target parameters and the frequency of occurrences of the
hottest days is assessed. The study presents a case study of South Africa in which the data for
the non-winter season (September–April of each year) are used. The meteorological data
used are the AMDT that are collected by the South African Weather Service and provided by
Eskom. The estimation of the shape parameter reveals evidence of a Weibull class as an
appropriate distribution for modelling AMDT in South Africa. The extreme quantiles for
specified return periods are estimated using the quantile function and the best model is
chosen through the use of the deviance statistic with the support of the graphical diagnostic
tools. The Entropy Difference Test (EDT) is used as a specification test for diagnosing the fit
of the models to the data.
