Utilize our Gumbel Distribution Calculator to determine probabilities of extreme events. Understand the likelihood of maximums or minimums occurring in various datasets. This tool is crucial for hydrology, finance, and engineering applications, helping you assess risk and plan for rare occurrences like floods or market peaks.
Formula:
The Gumbel distribution, a type of extreme value distribution, is characterized by two parameters: the location parameter (μ) and the scale parameter (β).
Probability Density Function (PDF):
f(x; μ, β) = (1/β) · e-(x - μ)/β · e-e-(x - μ)/β
Cumulative Distribution Function (CDF):
F(x; μ, β) = e-e-(x - μ)/β
- x: The specific value for which to calculate the probability or cumulative probability.
- μ (mu): The location parameter, influencing the peak's position.
- β (beta): The scale parameter, affecting the spread of the distribution (β > 0).