The smallest extreme value distribution is a limiting distribution for the minimum of a very large collection of random observations from the same arbitrary distribution. The smallest extreme value distribution describes extreme phenomena such as the minimum temperature, rainfall during drought, etc.
The largest extreme value distribution is a limiting distribution for the maximum of a very large collection of random observations from the same arbitrary distribution. The largest extreme value distribution describes extreme phenomena such as extreme wind velocities, large insurance losses, etc.
The extreme value distribution are described by location and scale parameters.
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Smallest extreme value distribution |
Largest extreme value distribution |
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The smallest extreme value distribution is skewed to the left. For example, the distribution of metal tensile strength is often skewed to the left with a few weak samples to the left and a majority with strengths at the upper tail. |
The largest extreme value distribution is skewed to the right. For example, the distribution of the water levels in a river over time is often skewed to the right with a few cases of extreme water levels to the right and a majority of water levels in the lower tail. |
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