## DISTRIBUCION GUMBEL PDF

Distribución Gumbel. Función de distribución: Desviación estándar: Moda de la distribución. La probabilidad de ocurrencia del evento x>xT. Para una variable. tion function (Gumbel copula multivariate simulation) and estimation functions ( Maxi- mum Likelihood Estimation, Inference For Margins. Transcript of Distribución Gumbel. Es utilizada para modelar la distribución del máximo (o el mínimo), por lo que se usa para calcular valores.

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In probability theory and statisticsthe Gumbel distribution Generalized Extreme Value distribution Type-I is used to model the distribution of the maximum or the minimum of a number of samples of various distributions. 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 distribycion extreme earthquake, flood or other natural disaster will occur. The potential applicability of the Gumbel distribution to distrobucion the distribution of maxima relates to extreme value theorywhich indicates that it is likely to be useful if the distribution of the underlying sample data is of the normal disgribucion exponential type.

## File:Gumbel-Density.svg

The rest of this article refers to 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. It is also known as the log- Weibull distribution and the double exponential distribution a term that is alternatively sometimes used to refer to the Laplace distribution.

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## Gumbel distribution

It is related to the Gompertz distribution: In the latent variable formulation of the multinomial logit model — common in discrete choice theory — the errors of the latent variables follow a Gumbel distribution. This is useful because the difference of two Gumbel-distributed random variables has a logistic distribution. The Gumbel distribution is named after Emil Julius Gumbel —based on his original papers describing the distribution.

The cumulative distribution function of the Gumbel distribution is. Theory related to the generalized multivariate log-gamma distribution provides a multivariate version of the Gumbel distribution.

In pre-software times probability paper was used to picture the Gumbel distribution see illustration.

In the paper the horizontal axis is constructed at a double log scale. The vertical axis is linear.

### Gumbel distribution – Wikipedia

When distribution fitting software like CumFreq became available, the task of plotting the distribution was made easier, as is demonstrated in the section below. Gumbel has shown that the maximum value or last order statistic in a sample of a random variable following an exponential distribution approaches the Gumbel distribution closer with increasing sample size.

In hydrologytherefore, the Gumbel distribution is used to analyze such variables as monthly and annual maximum values of daily rainfall and river discharge volumes, [3] and also to describe droughts. Therefore, this estimator is often used as a plotting position. In number theorythe Gumbel distribution approximates the number of terms in a random partition of an integer [8] as well as the trend-adjusted sizes of maximal prime gaps and maximal gaps between prime constellations.

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In machine learningthe Gumbel distribution is sometimes employed to generate samples from the categorical distribution.