The Topp-Leone generalized extreme value distribution: Extreme value analysis and return level estimation of the PM2.5 in Chiang Mai, Thailand

Abstract

In this paper, an extension of the generalized extreme value (GEV) distribution called the Topp Leone-GEV (TL-GEV) distribution is applied. The TL-GEV distribution has four parameters (λ, μ, σ, ξ), and it has the three named sub-models TLGumbel (for ξ = 0), TL-Fréchet (for ξ > 0), and TL-reversed Weibull (for ξ 0 or TLFréchet distribution can be considered competitive. The TL-GEV distribution is an alternative flexible way to analyze any extreme values and to estimate the return level, because the additional parameter λ provides flexibility to the distribution affecting its skewness and kurtosis.

Keywords

• extreme value theory
• t-x family of distributions
• topp leone-generalized extreme value distribution
• pm2.5
• return level