Journal of Statistics Applications & Probability

Author Country (or Countries)

South Africa


In studying natural hazards or disasters that occur due to temperature extremes such as heat waves and cold waves, it is crucial to understand the underlying distributions of the maximum and minimum temperatures at a particular site or region. The present study intends to investigate the parent distributions of maximum and minimum temperatures at various sites in the Limpopo province of South Africa. The parent distributions were investigated at four meteorological stations in Limpopo province, namely: Mara (1949-2018), Messina (1934-2009), Polokwane (1932-2018) and Thabazimbi (1994-2018). Four candidate parent distributions; normal, lognormal, gamma and Weibull distributions, were fitted to the average monthly maximum and minimum daily temperatures. Prior to the selection of the parent distributions, the data set at each station was subjected to normality test using the Shapiro-Wilk (SW) and Jarque-Bera (JB) tests. The normality tests have revealed that the maximum and minimum temperature data series at all the stations do not follow a normal distribution. Akaike information criterion (AIC) and Bayesian information criterion (BIC) were used to select the best fitting distribution at a particular site. The parent distribution with the lowest value of AIC and BIC was chosen as the best fitting distribution for the data. Goodness-of-fit diagnostic tests such as the Q-Q plots, P-P plots, empirical and theoretical density and cumulative distribution function (CDF) plots were conducted on the selected and/or competing candidate distributions. The findings reveal that short-tailed distributions in the Weibull domain of attraction, which include the Weibull distribution, are the best fitting parent distributions for both maximum and minimum temperature series at all the stations. Furthermore, a generalised extreme value (GEV) distribution was fitted to all the data set for each station in order to establish and validate whether the Weibull family is indeed a good fit to the data. The GEV distribution findings further confirmed the Weibull class as the parent distribution for all the stations in the study. The Mann-Kendall test and time series plots trend analysis findings have shown that there is a downward and upward long-term trend in minimum and maximum temperature data, respectively. Future studies will look into the possibility of applying both univariate and multivariate extreme value theory (MEVT) techniques to investigate further whether these climatic changes in mean monthly temperature can indeed be attributed to global warming and other natural modes of interdecadal variability

Suggested Reviewers


Digital Object Identifier (DOI)