| Revision as of 21:00, 17 July 2003 editRselsick (talk | contribs)3 editsNo edit summary | Revision as of 21:42, 17 July 2003 edit undoJiang (talk | contribs)43,437 editsmNo edit summaryNext edit → | ||
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| ⚫ | 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 | ||
| THE GUMBEL DISTRIBUTION | |||
| ⚫ | 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. | levels , floods and wind velocities. | ||
| It is sometimes called the Fisher-Tippet Distribution and is defined as ; | It is sometimes called the Fisher-Tippet Distribution and is defined as ; | ||
| p=exp(-exp((A-x)/B) | p=exp(-exp((A-x)/B) | ||
| A more practicle way of using the distribution could be | A more practicle way of using the distribution could be | ||
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| Q3=A-B*ln(-ln(.75)) | Q3=A-B*ln(-ln(.75)) | ||
| The mean is A+g*B 'g=Eulers constant = .57721 | The mean is A+g*B 'g=Eulers constant = .57721 | ||
Revision as of 21:42, 17 July 2003
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-Tippet Distribution and is defined as ;
p=exp(-exp((A-x)/B)
A more practicle 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