# Questions tagged [gumbel-distribution]

The Gumbel distribution (or generalized extreme-value distribution type I) is used in modeling of extrema.

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### Why does the best fitting Weibull distribution for this survival data deviate further from the actual data than a poorly fit distribution?

I started working with the Gumbel distribution and fit it to the lung dataset to try it out. I then compared it with the survival curve using the Weibull ...
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### Is there a clean way to derive the start parameters for running the fitdist() function for the Gumbel distribution?

I've begun working with the Gumbel distribution and started with the example in the package documentation at https://cran.r-project.org/web/packages/fitdistrplus/fitdistrplus.pdf. For the Gumbel ...
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### How to calculate Gumbel with LMoments and GEV with method of moments

I need to calculate the values for certain return periods of a flood event (up to 5000). It has to be GEV with method of moments and Gumbel with L-Moments. But I am not sure about how to calculate ...
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### Is there an intuition to the mean of a Gumbel distribution being the Euler constant vis-à-vis the modeling of extreme events?

The derivation is pure mechanistic integration as in here, and it doesn't come as a surprise to find the Euler constant in a distribution such as $\Lambda(x)=e^{-e^{-x}}$. However, the Euler constant ...
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### Standard error with maximum likelihood estimation

ASTM E2238 describes the prediction of the largest inclusion in a polished steel surface of 150,000 mm² based on a Gumbel distribution of the largest inclusions measured in each of 24 polished ...
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### negative values for AIC and BIC

I am trying to fit a gumbel distribution using MLE for the following 10 data points. DATA=(3.62,3.76,3.57,3.56,3.61,3.77,3.46,3.6,3.39,3.74) The problem is that the ...
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### KL divergence for Generalized Extreme Value distribution

I have found a derivation for the Kullback–Leibler divergence between 2 Gumbel distributions here: http://www.mast.queensu.ca/~communications/Papers/gil-msc11.pdf on page 64 That document also has a ...
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### Convergence maximum of Normal rv to gumbel through simulation (metropolis hastings)

I would like to see the convergence of an order statistic to its respective Extreme Value attractor by simulating with the Metropolis Hastings algorithm (I am self-studying MCMC algos). I was trying ...
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### Why do we need the temperature in Gumbel-Softmax trick?

Assuming a discrete variable $z_j$ with unnormalized probability $\alpha_j$, one way to sample is to apply argmax(softmax($\alpha_j$)), another is to do the Gumbel trick argmax($\log\alpha_j+g_j$) ...
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### Interpret the result of a fitted non-stationary Gumbel model

I have a dataset on wildfires that I fitted to a Gumbel distribution with a set of covariates (using the gevrFit function in the eva package in R). The result of ...
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### Simulate >2 variables from Gumbel Copula

I'm trying to simulate multiple random variables with different taus from the Gumbel copula. For the normal copula it's pretty simple, eg: ...
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### Extreme value distribution for univariate normal: Derive parameters of the Gumbel [duplicate]

I have a question regarding the extreme value distribution corresponding to i.i.d. samples $X_i$ from a normal distribution, say $X_i\sim N(\mu, \sigma^2)$. According to the theorem of Fisher-Tippett-...
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### Mean and Standard deviation of Gumbel distributions subtraction

I know that two normal distributions can be subtracted and get a new distribution with a mean of $\bar{x} = \bar{x}_1-\bar{x}_2$ and a standard deviation of $\sigma = \sqrt{\sigma_1^2 + \sigma_2^2}$. ...
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### t-test with logistic and Gumbel distributions

I know that one of the basic assumptions of a t-test is that the data is drawn from a Gaussian distribution. Using an Anderson-Darling test, I've found that the datasets I am working with are either ...
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### CDF for Correlated Gumbel Distribution in Nested Logit simulation

I am interested in estimating a nested logit model following McFadden (1978)'s formulation. It is simple to numerically verify the result in a standard situation with independently drawn error terms, ...