Research On The Poisson Point Process Models Of Haze And Their Stochastic Characteristics

Haze is a kind of atmospheric pollution phenomenon,which harms the development of national economy,the life of people,human health,traffic and so on.The number of haze is considered to be a homogeneous Poisson process in a fixed time interval.In this paper,we first discuss the basic theories of Poisson point process.Then,we establish the one-variate marked Poisson point process model that the level of the haze is marked value and the two-variate marked Poisson point process model that the level of the haze and the corresponding duration of the haze are marked values.Then we give the four model test methods and one estimation method for continuous observation data in a fixed time interval.Finally we collect the data of the haze in the Beijing in the past three years.We get the estimates of the models by the parameter estimation method.We calculate probability of the haze occurrence in the year and each season and use the mathematical expectation of compound Poisson process to get the average days of heavy haze in the year and each season in Beijing.According to the time interval of Poisson process,we can get the average days that there is not occurring haze by calculating mathematical expectation of the exponential distribution.Last we establish a loss function of the haze and give the formulas of the damage of haze.