Comparison of kernel density function in detecting effects of daily emission of Sulphur (IV) oxide from an industrial plant

Abstract

Air pollution is a major concern of environmentalists because of the importance of air to man and other living organisms. This paper is about the investigation on the effects of daily emission of Sulphur (IV) oxide from an industrial pollutant using a nonparametric estimator which is the kernel estimator. Nonparametric estimators are free from distributional assumptions owing to the fact that most real-life data are not from a particular family of distribution. The functionality of this estimator is contingent on the smoothing parameter also called the bandwidth that determines the degree of the smoothness applied when analyzing the data. The bandwidth is extrapolated by minimizing the asymptotic mean integrated squared error which is the objective function of the kernel estimator. In this investigation, we selected some kernel functions of the beta family with the Gaussian kernel and obtained their bandwidths or smoothing parameters with respect to their distribution. The result of the analysis showed that an increase in number of tons of Sulphur (IV) oxide was associated with higher concentration level of the gas which suggests a potential danger of the gas to humans, animals and plants in the environment.