# Extreme Value Modeling of Daily Maximum Temperature with the r-Largest Order Statistics

## Authors

• Piyapatr Busababodhin Department of Mathematics, Mahasarakham University, Mahasarakham, Thailand
• Monchaya Chiangpradit Department of Mathematics, Mahasarakham University, Thailand
• Nipada Papukdee Department of Mathematics, Mahasarakham University, Thailand
• Jiraphon Ruechairam Department of Mathematics, Mahasarakham University, Thailand
• Kettida Ruanthaisong Department of Mathematics, Mahasarakham University, Thailand
• Pannarat Guayjarempanishk Faculty of Interdisciplinary Studies, Nong Khai Campus, Khon Kaen University, Thailand

## Keywords:

generalized extreme value distribution, generalized extreme value distribution for the r largest order statistics, return level, deviance statistic

## Abstract

The aim of this study was to model the average daily maximum temperature in the north of Thailand including Mae Hong Son, Nan and Uttaradit which are the first-three maximum temperature provinces in Thailand. These data sets were collected during 1984–2018 by the Meteorological Department of Thailand.  Many researchers usually analyzed extreme value data by using the generalized extreme value distribution and focused on the first order of maximum value.  This interested the researcher to create a model with the generalized extreme value distribution for the r-largest order statistics with different orders such as r = 2, 3, 4, …, n for n is the number of data and compare the model of the maximum value of any sequence with the deviance statistics. The researcher would check the precision of the best model and the modified predicted absolute error. The researcher analyzed the data with “EVA” package in the R program. The results showed that the best model is the weibull distribution for the average daily temperature data from station of Nan Meteorological and Nan Sorkorsor Meteorological when r = 4, Mae Hong Son Meteorological and Uttaradit Meteorological when    r = 3 and Mae Sariang Meteorological when r = 2. In addition, the best model is the gumbel distribution for the average daily temperature data of Tha Wang Pha Meteorological station when r = 4, and Thung Chang Meteorological station when r = 2.  Furthermore, based on return levels of various return periods, the average daily maximum temperature in the north of Thailand was found that Mae Hong Son Meteorological station had the highest return level of maximum temperature for each return period.  Therefore, to solve and prevent the problems of temperature increase, Mae Hong Son Meteorological station should be the first considered.