Modeling the stochastic dependence of air pollution index data

Abstract

The air pollution index (API) is a common tool, which is often used for determining the quality of air in the environment. In this study, a discrete-time Markov chain model is applied for describing the stochastic behaviour of API data. The study reported in this paper is conducted based on the data collected from Klang city in Malaysia for a period of 3 years (2012–2014). Based on the API data, we considered a five-state Markov chain for depicting the five different states of the air pollution. We identified the Markov chain is an ergodic Markov chain and determined the limiting distribution for each state of the air pollution. In addition, we have identified the mean first passage time from one state to another. Based on the limiting distribution and the mean return time, we found that the risk of occurrences for unhealthy events is small. However, the risk remains notably troubling. Therefore, the standard of air quality in Klang falls within a margin that is considered healthy for human beings.