Modeling the Characteristics of Unhealthy Air Pollution Events: A Copula Approach
Abstract
:1. Introduction
2. Study Area and Data
3. Copula Description of Air Pollution Characteristics
4. Copula Models
4.1. Clayton Copula
4.2. Ali–Mikhail–Haq (AMH) Copula
4.3. Frank Copula
4.4. Plackett Copula
4.5. Gumbel–Hougaard (GH) Copula
4.6. Joe Copula
5. Parameter Estimation and Model Selection
5.1. Pseudo Maximum Likelihood Estimation (Pseudo-MLE)
5.2. Cross-Validation Copula Information Criterion (cvCIC)
6. Results and Discussion
7. Conclusions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Variable | Mean | Median | Min. Value | Max. Value | Std. Deviation | Skewness | Kurtosis |
---|---|---|---|---|---|---|---|
Duration (hours) | 21.39 | 3.00 | 1.00 | 224.00 | 64.81 | 2.78 | 9.23 |
Severity | 2876.50 | 367.00 | 102.00 | 36,677.00 | 15,193.68 | 3.38 | 13.12 |
Variable | Fitted Distribution | KS-Statistic | p-Value |
---|---|---|---|
Duration | Exponential | 0.3843 | 0.0000 |
Gamma | 0.1834 | 0.0009 | |
Lognormal | 0.1877 | 0.0006 | |
Weibull | 0.2227 | 0.0002 | |
Severity | Exponential | 0.3973 | 0.0000 |
Gamma | 0.2969 | 0.0000 | |
Lognormal | 0.1834 | 0.0009 | |
Weibull | 0.2139 | 0.0005 |
Copula Model | Parameter Estimate (θ) | cVCIC | Kendall’s τ |
---|---|---|---|
Clayton | 22.85 | 49.108 | 0.9195 |
Ali–Mikhail–Haq | 1 | 35.689 | 0.3333 |
Frank | 48 | 142.708 | 0.9195 |
Placket | 846.5 | 221.530 | 0.9195 |
Gumbel | 12.42 | 199.361 | 0.9194 |
Joe | 25.38 | 255.258 | 0.9195 |
Duration Size | API Severity | Joint OR Return Period, (Days) | Joint AND Return Period, (Days) | Conditional D|S Return Period, (Days) | Conditional S|D Return Period, (Days) |
---|---|---|---|---|---|
50-h | 100 | 4.4 | 34.4 | 34.6 | 268.5 |
1000 | 10.8 | 34.4 | 84.3 | 268.5 | |
10,000 | 34.4 | 56.4 | 720.9 | 439.9 | |
20,000 | 34.4 | 135.4 | 4153.6 | 1056.0 | |
30,000 | 34.4 | 406.3 | 4328.5 | 3168.0 | |
80-h | 100 | 4.4 | 56.4 | 56.7 | 721.1 |
1000 | 10.8 | 56.4 | 138.1 | 721.1 | |
10,000 | 54.8 | 58.2 | 743.2 | 743.2 | |
20,000 | 56.4 | 135.4 | 4153.6 | 1730.7 | |
30,000 | 56.4 | 406.3 | 7382.4 | 5192.0 | |
100-h | 100 | 4.4 | 101.6 | 102.0 | 2336.4 |
1000 | 10.8 | 101.6 | 248.6 | 2336.4 | |
10,000 | 56.4 | 101.6 | 1297.9 | 2336.4 | |
20,000 | 101.5 | 135.5 | 4153.9 | 3115.4 | |
30,000 | 101.6 | 406.3 | 7382.4 | 9345.6 | |
120-h | 100 | 4.4 | 169.3 | 170.0 | 6490.0 |
1000 | 10.8 | 169.3 | 414.2 | 6490.0 | |
10,000 | 56.4 | 169.3 | 2163.1 | 6490.0 | |
20,000 | 135.4 | 169.3 | 5193.5 | 6491.8 | |
30,000 | 169.3 | 406.3 | 7382.4 | 15,576.0 | |
150-h | 100 | 4.4 | 225.7 | 226.7 | 11,537.9 |
1000 | 10.8 | 225.7 | 552.3 | 11,537.9 | |
10,000 | 56.4 | 225.7 | 2884.1 | 11,537.9 | |
20,000 | 135.4 | 225.7 | 6922.7 | 11,537.9 | |
30,000 | 225.7 | 406.3 | 7382.4 | 20,768.1 |
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Masseran, N. Modeling the Characteristics of Unhealthy Air Pollution Events: A Copula Approach. Int. J. Environ. Res. Public Health 2021, 18, 8751. https://doi.org/10.3390/ijerph18168751
Masseran N. Modeling the Characteristics of Unhealthy Air Pollution Events: A Copula Approach. International Journal of Environmental Research and Public Health. 2021; 18(16):8751. https://doi.org/10.3390/ijerph18168751
Chicago/Turabian StyleMasseran, Nurulkamal. 2021. "Modeling the Characteristics of Unhealthy Air Pollution Events: A Copula Approach" International Journal of Environmental Research and Public Health 18, no. 16: 8751. https://doi.org/10.3390/ijerph18168751