Modelling annual maximum temperature of India: a distributional approach

Abstract

A random variable can take very large or very small values known as extreme values. In some instances, the researcher’s interest lies mainly on these extreme values like maximum (or minimum) temperature, maximum (or minimum) amount of precipitations, maximum level of flood water, maximum (or minimum) wind speed, maximum (or minimum) level of disease, or pest infestation in a particular crop or season. These types of extreme values can be modelled by generalized extreme value (GEV) distribution, theorized by McFadden in 1978. The type I GEV distribution, i.e. Gumbel distribution, has been extensively studied by many authors, but due to its constant skewness and kurtosis, it has limited practical application. To this end, different generalizations of Gumbel distribution have been proposed in different pieces of literature. In this manuscript, generalized Gumbel (GG) distribution is obtained from generalized multivariate Gumbel (GMVGB) distribution specified in Demirhan and Hamurkaroglu (Journal of Statistical Planning and Inference 141(Adeyemi and Ojo 2003):1141-1152, 2011) and different properties of this distribution have been derived. The continuous increasing of atmospheric concentration of greenhouse gases, mainly due to human activity, has led to global climate change. Climate change can in turn modify the occurrence and intensity of extreme weather and climate events—heat waves and sea-level rise. In the present study, one such climatic variable, i.e. the annual maximum temperature data of India, has been taken for the period of 1901 to 2017 and various extreme value distributions, namely GEV, Gumbel and GG, have been fitted. The obtained results indicate that the GG distribution is better fitted than the other two competing distributions.