# Questions tagged [extreme-value]

Extreme values are the largest or the smallest observations in a sample; e.g., the sample minimum (the first order statistic) and the sample maximum (the n-th order statistic). Associated with extreme values are asymptotic *extreme value distributions.*

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### How to deal with outliers in panel data? [closed]

When we have cross-sectional data, we can easily detect and remove outliers. But how should one approach outliers when we are dealing with panel data? Since we have $i$ entities and $t$ times periods, ...
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### How to simulate variability (errors) in fitting a gamma model to survival data by using a generalized minimum extreme value distribution in R?

As shown below and per the R code at the bottom, I plot a base survival curve for the lung dataset from the survival package ...
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### Does the following distribution converge to anything?

Consider the following process for generating a random sample: Sample $X_1, X_2, \dots, X_n \sim \mathcal{N}(0,1)$ Compute $M = \max\limits_i |X_i|$ Scale the values to get $Z_i = X_i / M$ Can we ...
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### How to assign reasonable scale parameters to randomly generated intercepts for the Weibull distribution?

This is a follow-on to post Correctly simulating an extreme value distribution for survival analysis?, as I work towards adaptation of that code to the Weibull distribution. In the below code I ...
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### Resource recommendation for extreme value theory

I'm look to learn about extreme value theory, starting from univariate case and then moving onto the multivariate case. I have tried the textbook by de Haan, but I'm constantly lost trying to read the ...
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### Correctly simulating an extreme value distribution for survival analysis?

In the image and per the code at the bottom of this post, I plot survival curves for the lung dataset from the survival package using a fitted exponential ...
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### Identifiability of a bivariate normal distribution with identified minimum

I am suffering from to understand a proof of a paper. (Nádas, Arthur. "The distribution of the identified minimum of a normal pair determines' the distribution of the pair." Technometrics 13....
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### Is modeling the extreme value of a distribution a basic probability result?

I was reading briefly about the field of EVT - extreme value theory, and the associated distributions that arise from modeling the maximum of a finite sample. It's not quite clear to me the nature of ...
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### Is every probability distribution also the distribution of the maximum of several i.i.d. random variables?

I found the following result used in this paper, but it was just claimed without proof and it seems extremely strong to me, so I would like a proof, or at least a reference, of a proof. Let $D$ be ...
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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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### Calculating probability related to maximum of random variables

Let $X_1, X_2, \cdots, X_n$ be non-negative continuous iid random variables. The goal is to find the probability: \begin{align*} \Pr(\max_{k+1 \leq i \leq j } X_i < \max_{1 \leq i \leq k }X_i) \end{...
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### What can be concluded when standard deviation plus mean exceeds largest value?

The sum of the mean and standard deviation of a non-normal distribution can exceed the value of the largest sample. For a good explanation of why, see Can mean plus one standard deviation exceed ...
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### How to choose the wanted root of the maximum likelihood function when there are multiple roots?

I need to estimate a parameter of a distribution but I don't have an explicit estimator. I decided to do a partition of the interval range for the parameter and use the newton-raphson method to find ...
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### CDF of max of $n$ cauchy variates

Suppose $X_1,X_2,\cdots,X_n$ are iid copies of a standard cauchy variate with pdf $$f(x)=\frac{1}{\pi(1+x^2)},0<x< \infty.$$ Define: $$Y=1+ \underset{1 \leq i \leq n}\max X_i.$$ I want to ...
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