Estimating Extreme Quantiles of the Maximum Surface Air Temperatures for the Sir Seretse Khama International Airport Using the Generalized Extreme Value Distribution
American Journal of Theoretical and Applied Statistics
Volume 5, Issue 6, November 2016, Pages: 365-375
Received: Oct. 10, 2016; Accepted: Oct. 22, 2016; Published: Nov. 14, 2016
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Authors
Thuto Mothupi, Department of Statistics, University of Botswana, Gaborone, Botswana
Wilson Moseki Thupeng, Department of Statistics, University of Botswana, Gaborone, Botswana
Baitshephi Mashabe, Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, Palapye, Botswana
Botho Mokoto, Department of Risk Management, Insurance and Actuarial Science, Ba Isago University, Gaborone, Botswana
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Abstract
In this paper, extremes of quarterly maximum surface air temperature are modelled by employing the block maxima approach to extreme value analysis. The aim of the paper is to predict the future behaviour of the quarterly maximum surface air temperatures by estimating their high quantiles using the generalized extreme value distribution, an extreme value distribution usually used to model block maxima. The data are derived from monthly maximum surface air temperatures recorded at the SSSK International Airport Weather Station from January 1985 to December 2015. The Jarque-Bera normality test is performed on the data, and shows that the quarterly maximum temperatures do not follow a normal distribution. The Seasonal Mann-Kendall test detects no monotonic trends for the quarterly maximum temperatures. The Kwiatkowski- Phillips-Schmidt-Shin test indicates that the data are stationary. Parameter values of the generalized extreme value distribution are estimated using the method of maximum likelihood, and both the Kolmogorov-Smirnov and Anderson-Darling goodness of fit tests show that the distribution gives a reasonable fit to the quarterly maximum surface air temperatures. Estimates of the T-year return levels for the return periods 5, 10, 25, 50, 100, 110 and 120 years reveal that the surface air temperature for the SSK International Airport will be increasing over the next 120 years.
Keywords
Maximum Temperature, Extreme Value, Return Level, Generalized Extreme Value Distribution, Stationarity, Climate Change
To cite this article
Thuto Mothupi, Wilson Moseki Thupeng, Baitshephi Mashabe, Botho Mokoto, Estimating Extreme Quantiles of the Maximum Surface Air Temperatures for the Sir Seretse Khama International Airport Using the Generalized Extreme Value Distribution, American Journal of Theoretical and Applied Statistics. Vol. 5, No. 6, 2016, pp. 365-375. doi: 10.11648/j.ajtas.20160506.16
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Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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