All Questions
Tagged with extreme-value gumbel-distribution
23 questions
1
vote
2
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149
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Distribution of a random variable conditional on its being a maximum or not
Consider the random variables $\epsilon_1,\dots, \epsilon_D$ defined on the probability space $(\Omega, \mathcal{F}, P)$. Assume they are continuous. Let
$$
Y=\sum_{d=1}^D d\times \mathbb{1}\{\...
- 935
1
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0
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30
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Multinomial Logit Extension
The derivation of the multinomial logit probabilities depends on the difference of two Type 1 extreme value (Gumbel) random variables following a logistic distribution. We say the unobserved utility ...
- 31
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31
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Validity of bootstrapping for estimation of annual maxima distribution
I am working with a large timeseries (millions data points) spread across 5 years from which I would like to estimate the annual maxima distribution and subsequently a quantile of this distribution.
...
- 1
0
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0
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57
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Empirically estimating extremal coefficient using minima of Fréchet margins
I recently came across a paper which uses the following formula to empirically estimate the extremal correlation coefficient $\chi_{ij}$ between two variables $x$ and $y$ as follows:
$$ \chi_{xy} = \...
1
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0
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48
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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 ...
- 11
2
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0
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84
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Calculating confidence Interval for a return time curve, via non-parametric bootstrapping
I have some precipitation data (yearly extremes), which I have fit with a Gumbel distribution (CDF), from which I have calculated a return time distribution. I want to calculate the 95% confidence ...
- 21
0
votes
1
answer
198
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Fitting Gumbel distribution based the maximal observation
Assume that we only consider $$G(x)=\exp(-\exp(\frac{x-\mu}{\sigma}))$$ is the Gumbel distribution.
Question: Suppose we have a set of maximum values $\{Y_i\}_{i=1}^m$, why can the article directly (...
- 747
4
votes
1
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540
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Can we fit extreme value distribution by build-in package?
I try to find a package in R to fit Gumbel distribution by Block Maxima Approach using maximal likelihood function (see here)
$$
G(x; \mu , \sigma)=\exp[-e^{-\frac{x-\mu}{\sigma}}].
$$
The block ...
- 747
2
votes
1
answer
398
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Why does Gumbel distribution have two different expressions?
Let $X_1,X_2,\dots,X_n$ be iid random variables with distribution function $F(x)$ and $M_n:=\max\{X_1,\dots,X_n\}$. By the extreme value theorem, there exist two sequences of real numbers $a_n>0$ ...
- 747
2
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2
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235
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Fourth class of extreme-value distributions?
The generalized extreme-value distribution encompasses three classes of distributions:
Frechet, which are regularly varying, infinite right limit.
Gumbel, which are not regularly varying, infinite ...
- 533
0
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0
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417
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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 ...
- 61
2
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1
answer
395
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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 ...
3
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0
answers
555
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Convergence rate of the maximum of Weibull random variables to a Gumbel distribution
Given a sequence of iid samples $X_1, \dots, X_n,$ where each $X_i$ comes from a Weibull distribution with shape parameter $k$ and scale parameter $\lambda$. Then it is a well-known result that the ...
- 93
1
vote
1
answer
95
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Simulating Draws of Multivariate EV-Type Distribution
Let $\varepsilon = [\varepsilon_1,...,\varepsilon_J]$ be a random vector that we can partition into $K$ disjoint subvectors. $\varepsilon$ has this cdf:
\begin{equation} F(\varepsilon) = \exp \bigg[-\...
- 11
0
votes
1
answer
159
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Interpretation of a Gumbel distribution's results
I am using (essentially) the approach outlined in the paper "Statistical-based WCET estimation and validation" (http://drops.dagstuhl.de/opus/volltexte/2009/2291/pdf/Hansen.2291.pdf) to build a Gumbel ...
- 131
7
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1
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1k
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Extreme Value Theory - domains of attraction and techniques for evaluting a limit
We consider the gamma uniform G distribution as specified by
Torabi and Montazeri:
$$f(x) = \frac{1}{\Gamma (a)}\frac{g(x)}{[1-G(x)]^2}\left[\frac{G(x)}{1-G(x)}\right]^{a-1}\exp\left[\frac{G(x)}{1-G(x)...
- 309
2
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0
answers
135
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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 ...
- 21
5
votes
1
answer
487
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Extreme value theory: show that $ \lim_{n\rightarrow \infty}a_n $ exists and is finite
Well known facts in extreme value theory:
Let $\{X_i\}_{\forall i \in \{1,...,n\}}$ be i.i.d. random variables with cdf $F$. If there exists $\{a_n\}_{n\in \mathbb{N}}>0$, and $\{b_n\}_{n\in \...
- 935
1
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0
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364
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Normalising constant of the Gumbel in extreme value theory
Well known facts in extreme value theory:
Let $\{X_i\}_{\forall i \in \{1,...,n\}}$ be i.i.d. random variables with cdf $F$. If there exists $\{a_n\}_{n\in \mathbb{N}}>0$, and $\{b_n\}_{n\in \...
- 935
4
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0
answers
189
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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-...
- 41
4
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2
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121
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Extreme value distribution with unknown variance
Let $\{X_1,\ldots,X_n\}$ be a sequence of r.v. such that $X_i\sim N(0,\sigma^2)$.
It is usually stated in Extreme Value Theory textbooks that (for suitably chosen $a_n$ and $b_n$)
$$\mathbb{P}\left(\...
- 1,385
1
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0
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322
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Weibull, Gumbell and Extreme Value: from mean and variance to shape, scale and location parameter
I need to sample random numbers from Weibull, Gumbel and Generalized extreme value distributions. Of all of these distributions I know mean and variance. My question is: how can I determine these ...
- 253
3
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0
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1k
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Confidence intervals for extreme value distributions
I have wind data that i'm using to perform extreme value analysis (calculate return levels). I'm using R with packages 'evd', 'extRemes' and 'ismev'.
I'm fitting GEV, Gumbel and Weibull distributions,...
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