Details The Gumbel distribution gives the asymptotic distribution of the minimum value in a sample from a distribution such as the normal distribution. The asymptotic distribution of the maximum value, also sometimes called a Gumbel distribution, is implemented in the Wolfram Language as ExtremeValueDistribution. This behavior can be made quantitatively precise by analyzing the SurvivalFunction of the distribution. The Gumbel distribution is sometimes referred to as a type-1 extreme value distribution not to be confused with "the" extreme value distribution, implemented in the Wolfram Language as ExtremeValueDistribution , the doubly exponential distribution not to be confused with LaplaceDistribution , which may also be called doubly exponential , or the log-Weibull distribution cf. GumbelDistribution is one of four distributions along with FrechetDistribution , ExtremeValueDistribution , and WeibullDistribution classified under the general heading "extreme value distributions", all of which are used as tools for quantifying "extreme" or "rare" events i.

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Details The Gumbel distribution gives the asymptotic distribution of the minimum value in a sample from a distribution such as the normal distribution. The asymptotic distribution of the maximum value, also sometimes called a Gumbel distribution, is implemented in the Wolfram Language as ExtremeValueDistribution. This behavior can be made quantitatively precise by analyzing the SurvivalFunction of the distribution. The Gumbel distribution is sometimes referred to as a type-1 extreme value distribution not to be confused with "the" extreme value distribution, implemented in the Wolfram Language as ExtremeValueDistribution , the doubly exponential distribution not to be confused with LaplaceDistribution , which may also be called doubly exponential , or the log-Weibull distribution cf.

GumbelDistribution is one of four distributions along with FrechetDistribution , ExtremeValueDistribution , and WeibullDistribution classified under the general heading "extreme value distributions", all of which are used as tools for quantifying "extreme" or "rare" events i.

The Gumbel distribution is named for German mathematician Emil Julius Gumbel, who studied it in the late s as a limit distribution for the smallest order statistic i. Since its inception, the Gumbel distribution has been used to model a number of real-world phenomena, including human lifetimes, radioactive emissions, evolutionary genetic mutations, flood and seismic analyses, droughts, and catastrophic insurance losses.

The Gumbel distribution has also been used in number theory to approximate the number of terms in a partition of an integer see IntegerPartitions , as well as the sizes of record prime gaps.

RandomVariate can be used to give one or more machine- or arbitrary-precision the latter via the WorkingPrecision option pseudorandom variates from a Gumbel distribution. The mean, median, variance, raw moments, and central moments may be computed using Mean , Median , Variance , Moment , and CentralMoment , respectively.

DistributionFitTest can be used to test if a given dataset is consistent with a Gumbel distribution, EstimatedDistribution to estimate a Gumbel parametric distribution from given data, and FindDistributionParameters to fit data to a Gumbel distribution.

ProbabilityPlot can be used to generate a plot of the CDF of given data against the CDF of a symbolic Gumbel distribution and QuantilePlot to generate a plot of the quantiles of given data against the quantiles of a symbolic Gumbel distribution.

TransformedDistribution can be used to represent a transformed Gumbel distribution, CensoredDistribution to represent the distribution of values censored between upper and lower values, and TruncatedDistribution to represent the distribution of values truncated between upper and lower values.

CopulaDistribution can be used to build higher-dimensional distributions that contain a Gumbel distribution, and ProductDistribution can be used to compute a joint distribution with independent component distributions involving Gumbel distributions. The Gumbel distribution is related to several other distributions.

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## DistribuciĆ³n de Gumbel

This distribution might be used to represent the distribution of the maximum level of a river in a particular year if there was a list of maximum values for the past ten years. It is useful in predicting the chance that an extreme earthquake, flood or other natural disaster will occur. The potential applicability of the Gumbel distribution to represent the distribution of maxima relates to extreme value theory , which indicates that it is likely to be useful if the distribution of the underlying sample data is of the normal or exponential type. This article uses the Gumbel distribution to model the distribution of the maximum value. To model the minimum value, use the negative of the original values. The Gumbel distribution is a particular case of the generalized extreme value distribution also known as the Fisher-Tippett distribution.

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