Let {Tn } be a renewal process in R＋ representing the successive arrival times of some natural events. We studied this process by using a record process approach under the assumption that the interarrival times T,, =...Let {Tn } be a renewal process in R＋ representing the successive arrival times of some natural events. We studied this process by using a record process approach under the assumption that the interarrival times T,, = Tn, - Ta-1, n = 1, 2...are exponentially i.i.d （independent and identically distributed）. The goal is to test that the first observed events are sporadic events. For testing the hypothesis ＂sporadic＂ we used the non-parametric test based on the probability distribution of the statistic of the number of records N, among{Xx }k-1= where Xk = （ΔTk）-1. We showed that it is independent of the cumulative distribution of the observations and that it is exactly calculated for each n. We illustrated this statistic on a simulated trajectory and we compared it with descriptive smoothing methods. We studied an application to a data set as storms in France and US.展开更多
During the last decades, air pollution has become a serious environmental hazard. Its impact on public health and safety, as well as on the ecosystem, has been dramatic. Forecasting the levels of air pollution to main...During the last decades, air pollution has become a serious environmental hazard. Its impact on public health and safety, as well as on the ecosystem, has been dramatic. Forecasting the levels of air pollution to maintain the climatic conditions and environmental protection becomes crucial for government authorities to develop strategies for the prevention of pollution. This study aims to evaluate the atmospheric air pollution of the city of Zahleh located in the geographic zone of Bekaa. The study aims to determine a relationship between variations in ambient particulate concentrations during a short time. The data was collected from June 2017 to June 2018. In order to predict the Air Quality Index (AQI), Naïve, Exponential Smoothing, TBATS (a forecasting method to model time series data), and Seasonal Autoregressive Integrated Moving Average (SARIMA) models were implemented. The performance of these models for predicting air quality is measured using the Mean Absolute Error (MAE), the Root Mean Square Error (RMSE), and the Relative Error (RE). SARIMA model is the most accurate in prediction of AQI (RMSE = 38.04, MAE = 22.52 and RE = 0.16). The results reveal that SARIMA can be applied to cities like Zahleh to assess the level of air pollution and to prevent harmful impacts on health. Furthermore, the authorities responsible for controlling the air quality may use this model to measure the level of air pollution in the nearest future and establish a mechanism to identify the high peaks of air pollution.展开更多
文摘Let {Tn } be a renewal process in R＋ representing the successive arrival times of some natural events. We studied this process by using a record process approach under the assumption that the interarrival times T,, = Tn, - Ta-1, n = 1, 2...are exponentially i.i.d （independent and identically distributed）. The goal is to test that the first observed events are sporadic events. For testing the hypothesis ＂sporadic＂ we used the non-parametric test based on the probability distribution of the statistic of the number of records N, among{Xx }k-1= where Xk = （ΔTk）-1. We showed that it is independent of the cumulative distribution of the observations and that it is exactly calculated for each n. We illustrated this statistic on a simulated trajectory and we compared it with descriptive smoothing methods. We studied an application to a data set as storms in France and US.
文摘During the last decades, air pollution has become a serious environmental hazard. Its impact on public health and safety, as well as on the ecosystem, has been dramatic. Forecasting the levels of air pollution to maintain the climatic conditions and environmental protection becomes crucial for government authorities to develop strategies for the prevention of pollution. This study aims to evaluate the atmospheric air pollution of the city of Zahleh located in the geographic zone of Bekaa. The study aims to determine a relationship between variations in ambient particulate concentrations during a short time. The data was collected from June 2017 to June 2018. In order to predict the Air Quality Index (AQI), Naïve, Exponential Smoothing, TBATS (a forecasting method to model time series data), and Seasonal Autoregressive Integrated Moving Average (SARIMA) models were implemented. The performance of these models for predicting air quality is measured using the Mean Absolute Error (MAE), the Root Mean Square Error (RMSE), and the Relative Error (RE). SARIMA model is the most accurate in prediction of AQI (RMSE = 38.04, MAE = 22.52 and RE = 0.16). The results reveal that SARIMA can be applied to cities like Zahleh to assess the level of air pollution and to prevent harmful impacts on health. Furthermore, the authorities responsible for controlling the air quality may use this model to measure the level of air pollution in the nearest future and establish a mechanism to identify the high peaks of air pollution.
