| Revision as of 21:10, 19 July 2003 editMichael Hardy (talk | contribs)Administrators210,264 edits This article was deficient in context-setting and still needs work. I'll get to it ....← Previous edit | Revision as of 21:11, 19 July 2003 edit undoMichael Hardy (talk | contribs)Administrators210,264 edits This really ought to say what the Gumbel distribution _is_ before saying what it is _used_for_. I'll get to it at some point......Next edit → | ||
| Line 1: | Line 1: | ||
| 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 | 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. | ||
| 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 ; | ||
Revision as of 21:11, 19 July 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-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