Flexible Heavy Tail Distributions for Surface Ozone for Selected Sites in the United States of America

The generalized extreme value distribution, generalized Pareto distribution, Pareto type-I distribution, Pareto type-II distribution, Burr distribution, log-logistic distribution, Fréchet distribution, log-normal distribution, log-Cauchy distribution, Lévy distribution, and Dagum distribution are fitted to four data-sets consisting of surface-level ozone for Weaverville, California (WVR); Tundra Lab, Niwot Ridge, Colorado (TUN); South Pole, Antarctica (SPO); and Mauna Loa, Hawaii (MLO) sites in the USA. Based on the probability distribution with the smallest Akaike information criterion, Bayesian information criterion, corrected Akaike information criterion, mean square error, mean absolute deviation, and maximum deviation values and probability-probability plots, the Dagum distribution emerged as the best fitting distribution for Weaverville, the Burr distribution emerged as the best fitting distribution for Niwot Ridge and Mauna Loa, and the log-Cauchy distribution emerged as the best fitting distribution for the South Pole site. The value at risk for each of the ozone sites is given and a backtest based on the Kupiec test is used to verify the appropriateness of the selected distributions.