Bootstrap Method for Order Statistics and Modeling Study of the Air Pollution

Abstract

In this article, the block maxima (BM) and the peak over threshold (POT) methods are used to model the air pollution. A simulation technique is suggested to choose a suitable threshold value. The validity of the estimated models is checked by the Kolmogorov–Smirnov (K-S) test. A new efficient approach for modeling extreme values is suggested. Finally, the inconsistency and weak consistency of bootstrapping central and intermediate order statistics for an appropriate choice of re-sample size are investigated.

Keywords:

• Air pollution
• Bootstrap technique
• Generalized extreme value model
• Generalized Pareto distribution
• Kolmogorov–Smirnov test
• Weak consistency

Mathematics Subject Classification:

• Primary 62G32
• Secondary 62F40