On the Generalized Pareto Probability Density Function of the Mean Annual Rainfall of Katsina State

Abstract

This work was accomplished to assess the rainfall probability density function (pdf) of Katsina State and adopt the most parsimonious density function using 2003 – 2018 rainfall data from the Nigeria Institute of Meteorological Services. The data were subjected to cleaning, descriptive statistics and investigation of five distribution functions (General pareto, general extreme value, Gumbel maximum, Uniform and Normal distribution) through parameterizations. The results intimated that Daura experienced the highest mean annual rainfall ranging between 75.667 mm for 2003 and 82.417 mm for 2018. Both Dutsin-Ma and Safana local Government returned the least mean annual rainfall alternately and it ranged between 57.500 mm (2009 rainfall for Dutsin-Ma) and 67.167 mm for 2018 mean annual rainfall of Safana.  The order of performance of the five (5) prominent pdf in each of the sites differs but the Generalized Pareto distribution (GPD) ranked highest across all the sites. The distribution characteristics for the GPD (the most parsimonious of the pdf) are, mean = 61.15098 (Duara), 58.93371 (Dutsinma) and 79.20851 (Safana) and variance of 9212.603 (Duara), 6709.908 (Dutsinma) and 6687.102 (Safana).  The examination of the visual analysis of the residuals of the mean annual rainfall indicated that only the mean rainfall for Dutsin-Ma gave the most precise parameter estimates.