| Revision as of 14:08, 20 January 2004 editRselsick (talk | contribs)3 editsNo edit summary← Previous edit | Revision as of 01:59, 14 February 2004 edit undoThe Anome (talk | contribs)Edit filter managers, Administrators252,962 edits hmm. this needs workNext edit → | ||
| Line 15: | Line 15: | ||
| A more practical way of using the distribution could be | A more practical way of using the distribution could be | ||
| p=exp(-exp(-0.367*(A-x)/(A-M)) ;-.367=ln(-ln(.5)) | p=exp(-exp(-0.367*(A-x)/(A-M)) ;-.367=ln(-ln(.5)) | ||
| where M is the |
where M is the ]. To fit values one could get the median | ||
| straight away and then vary A until it fits the list of values. | straight away and then vary A until it fits the list of values. | ||
| Line 26: | Line 26: | ||
| ie Q1=A-B*ln(-ln(.25)) | ie Q1=A-B*ln(-ln(.25)) | ||
| The |
The median is A-B*ln(-ln(.5)) | ||
| Q3=A-B*ln(-ln(.75)) | Q3=A-B*ln(-ln(.75)) | ||
Revision as of 01:59, 14 February 2004
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.For exemple we would use it to find the maximum level of a river in a particular year if we had the list of maximum values for the past ten years.It is therefore usefull in predicting the chance that an earthquake, flood or other natural disaster will occur.
The distribution of the samples could be of the normal or exponential type. The Gumbel distribution, and similar distributions, are used in extreme value theory.
In particular, the Gumbel distribution is a special case of the Fisher-Tippett distribution, also known as the log-Weibull distribution, whose cumulative distribution function is
The Gumbel distribution is the case where μ = 0 and β = 1.
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 until 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
See also: