Mathematical and Statistical Analysis of Monthly Mean Temperature Trend in Pakistan

Abstract

Due to the temperature rises global warming has become very popular. Increasing of global temperature will disturb the agronomic sector, intensification some of the contagious diseases that may lead to high mortality rates in humans, high demand for electricity, water and food which ultimately affecting the economy of Pakistan.  The current research aims to study the best fitted probability distribution that describes the monthly mean temperature (MMT)  of four sites in Pakistan are Islamabad, Lahore, Muzaffarabad and Karachi based on secondary data sets which was collected from Pakistan Meteorological department Lahore for the period 1991 to 2020.  The Frechet, Weibull and Log-Logistic distributions are applied and the parameters of these distributions are estimated by maximum likelihood and Bayesian estimation methods. Additionally, Log-normal and Generalized Extreme value distribution are considered using the maximum likelihood estimation method to estimate the parameters. Moreover, the graphs of probability density functions also constructed for comparison purposes. The goodness of fit test and model selection criteria such as Kolmogorov-Smirnov test, Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) are used to measure the accuracy of the predicted data using theoretical probability distributions. The results show that four sites favor the candidate distributions based on the P-values of Kolmogorov-Smirnov test at 5 percent level of significance. However, Log-Logistic distribution is the best fitted as compare to other candidate probability distributions based on AIC and BIC values. Furthermore, quantiles are also calculated using maximum likelihood and Bayesian estimation methods and concluded that quantile estimates are closed to the observed MMT series on the basis of Log-Logistic distribution.
Keywords: Log-normal distribution, Generalized Extreme value distribution, Frechet distribution ,Weibull distribution, Log-Logistic distribution, Akaike Information Criterion, Bayesian Information Criterion, Kolmogorov-Smirnov test, Quantile estimation, Time series analysis.