The Slash Power Normal Distribution with Application to Pollution Data

Abstract

In this paper, we introduce a new slash distribution via the power normal distribution and uniform distribution. This new distribution, called the slash power normal distribution, models more appropriately the skewness and kurtosis of data than the power normal distribution. Moreover, the probability density function and the cumulative distribution function of the slash power normal distribution are derived and the density function curves with different parameters are given. We also study the basic properties of the moments, derive the maximum likelihood estimation of the parameters, and substantiate our arguments with numerical simulations. Finally, we model hourly measurements of sulphur dioxide concentrations of a station in Hong Kong by the slash power normal distribution, power normal distribution, and skew normal distribution and use the K-S test to evaluate the model fittings. The result demonstrates that the slash power normal distribution gives a better fit to the data.