The Gumbel distribution is a probability distribution used to model the distribution of the maximum (or minimum) values in a dataset. It is particularly useful in fields like meteorology and engineering for predicting extreme events, such as floods or material failure. The distribution is characterized by its two parameters: location and scale, which help define its shape. This distribution is part of the family of extreme value distributions and is often applied in reliability analysis and risk assessment. The Gumbel distribution can be represented mathematically, and its cumulative distribution function (CDF) allows for the calculation of probabilities related to extreme values.