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| In ] and ] the '''Gumbel distribution''' is used to find the minimum (or the maximum) of a number of samples of various distributions. These distributions could be of the normal or exponential type. It is used for the extreme values of water levels , floods and wind velocities. | In ] and ] the '''Gumbel distribution''' is used to find the minimum (or the maximum) of a number of samples of various distributions. These distributions could be of the normal or exponential type. It is used for the extreme values of water levels , floods and wind velocities. | ||
| It is sometimes called the '''Fisher- |
It is sometimes called the '''Fisher-Tippett distribution''' and is defined as | ||
| :<math>p = \exp(-\exp((A-x)/B).</math> | :<math>p = \exp(-\exp((A-x)/B).</math> | ||
Revision as of 19:12, 8 November 2003
In probability theory and statistics the Gumbel distribution is used to find the minimum (or the maximum) of a number of samples of various distributions. These distributions could be of the normal or exponential type. It is used for the extreme values of water levels , floods and wind velocities.
It is sometimes called the Fisher-Tippett distribution and is defined as
A more practical way of using the distribution could be
p=exp(-exp(-0.367*(A-x)/(A-M)) ;-.367=ln(-ln(.5))
where M is the Median.To fit values one could get the Median straight away and then vary A untill it fits the list of values.
Its variates(ie to get a list of random values) can be given as ;
x=A-B*ln(-ln(rnd))
Its percentiles can be given by ;
x=A-B*ln(-ln(p))
ie Q1=A-B*ln(-ln(.25))
The Median is A-B*ln(-ln(.5))
Q3=A-B*ln(-ln(.75))
The mean is A+g*B 'g=Eulers constant = .57721
The sd = B * Pi()* sqr(1/6)
Its mode is A