# 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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### What is the median of the minimum or maximum of multiple samples?

Suppose I have a variable with a known distribution, and suppose I sample that variable k times and record the minimum. If I repeat this many times, will the median of the minimum converge to a ...
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### analytical asymptotic approximation of the expected maximum, mean, and minimum distance of nearest neighbours in unit ball

Say I uniformly at random distribute $x = n^3$ (independent identically distributed) points in a ball of radius $r=1$ in $\mathbb{R}^3$. What can be said about the expected maximum, minimum, and mean ...
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### In a sum of high-variance lognormals, what fraction comes from the first term?

If $X_i \overset{\textrm{iid}}{\sim} \text{Lognormal}(0, \sigma^2)$ for $i=1,\ldots,n$ and $Y_1 = X_1 / \sum_{j=1}^n X_j$, then I would expect that a particular* limiting distribution of $Y_1$, ...
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### Declustering impact, stationarity and discretization

I have a seasonal time series, and I am considering declustering (before any other preprocessing steps) it using runs declustering. If I observe an extremal index of 1, can I claim that my data is i.i....
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### Does the mean of the maxima of a set of distributions converge?

This question is related to a recent one I posted. In that question I ask what statistic might best represent the central tendency of the true discrete distribution of a property for a sample for ...
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### What statistic best estimates the sample mean in case of missing data in a distribution?

I have samples of particles and am interested in the particle lengths. The problem is that the samples are assessed using image analysis. As the particles overlap, the measurements are incomplete and ...
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1 vote
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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 ...
279 views

### 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 ...
1 vote
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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 ...
1 vote
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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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1 vote
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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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