Extreme Value Theory

Extreme Value Theory

Extreme Value Theory (EVT) focuses on the asymptotic distribution of the maximum or minimum of a sample as the sample size becomes very large. It’s a key part of understanding risks in various domains such as finance, insurance, environmental science, and engineering, where understanding the behavior of tail-end events (extreme risks) is crucial. EVT is divided into two main types:

• Type I (Gumbel): For block maxima or minima of unbounded distributions.
• Type II (Fréchet): For maxima of distributions with a power-law tail.
• Type III (Weibull): For minima of distributions bounded from above.