Questions tagged [extreme-value]

Question 1

Let us consider a pair of random variables $y, x$ with a conditional distribution $p(y | x)$ and marginal distributions $p_Y(y), p_X(x)$. We observe an i.i.d. sample $D_x = \{x_i\}_{i = 1}^n$. The ...

Question 2

Why Generalized Pareto Distribution (GPD) MLE estimation of Tail Index fails? On the chart multiple simulation of the same $\text{StudentT}(\nu=4)$ with tail estimated with GPD estimator (blue lines). ...

Question 3

I am analysing a sample of size $n = 200$ that appears to follow a Student-$t$ distribution fixed by design. Fitting the model yields $\hat{\nu} = 10.22$ but with a relatively large standard error of $...

Question 4

There are lots of examples and posts of general rules to find normalizing constants for extreme value theory, see here and there for instance. However, these deal with normalizing to the asymptotic ...

Question 5

My goal is to estimate the market beta (so exposure of an asset returns to market shocks) in quantiles : $Q_{r_i|r_M} = a_0(\tau) + \beta_i(\tau)r_M+\varepsilon_i(\tau)$ where $r_i$ are asset returns (...

Question 6

What's an example of stochastic process $X_t$ on $[0,1]$(i.e. a random variable for each $t \in [0,1]$) such that For all $t$, $X_t \geq 0$ For all $t$, $\mathbb{E}[X_t] = 1$ $\mathbb{E}[\sup_{t \in [...

Question 7

Suppose I have a database of entities. The database has a column for the name of the entity, min A, max A, min B, max B. Where the min/max columns are the min/max for variables A and B. It is unknown ...

Question 8

Let say I want to estimate the number $N$ of balls in an urn by taking a sampling of $n$ balls (without replacement). The balls are numbered from $1$ to $N$ and let $Z$ denote the maximum of the ...

Question 9

I am performing a generalized extreme value analysis using about 20 years of data sampled every 1 minute. I am doing this in order to predict return levels at e.g. 1-in-50 and 1-in-100 intervals. The ...

Question 10

I am computing the Generalized Extreme Value distribution for a dataset containing about 15 years of data sampled every 5 seconds. I want to estimate the 1-in-50 or 1-in-100 year return level from the ...

Question 11

The Pickands-Balkema-de Haan theorem states that the conditional excess distribution function is well approximated by the generalized Pareto distribution (for high excesses and if the underlying RV's ...

Question 12

I am trying to find a confidence interval for ${\theta}/{ 2}$ with confidence level $1-\alpha$ (using quantiles at $p_1 = \alpha$ and $p_2 = 1$). So I take unbiased estimator for ${\hat{\theta}}/{2} =...

Question 13

Let $X_i$ be an iid draw from a Frechet distribution. Let $\alpha_i \in \mathbb{R}$. Is there an analytical expression of the distribution of $\alpha_1X_1 + \alpha_2X_2 + \alpha_3X_3$? That is, can I ...

Question 14

I am using the fevd() and lr.test() functions to examine precipitation using the extRemes R ...

Question 15

Consider the following random variable $$ Z=\min_i\{X_i+Y_i\} $$ for $-n\leq i\leq n$, where $X_i\overset{\mathrm{iid}}{\sim}\text{Exp}(\lambda)$, $Y_i\overset{\mathrm{iid}}{\sim}\text{Erlang}(|i|,\...

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Questions tagged [extreme-value]

Distribution of Y conditioned on the index of the minimum of X

Why GPD MLE (EVT) fails to estimate Tail Index for Student T?

Parametric bootstrap for a Student-t model when the degrees-of-freedom estimate has a very large standard error

Choosing normalizing constants for extreme value distributions for finite samples

Minimum number of observations quantile regression

An example of stochastic process $X_t$ on $[0,1]$ such that $\mathbb{E}[\inf_{[0,1]} \left|f(t)\right| X_t] = 0$

Classify sample based on min/max values [closed]

Confidence interval for the size of a population

Why does GEV fit sometimes not fit the tails well?

How to get 1-in-100 return period from GEV when using a block length shorter than a year?

Pickands-Balkema-De Haan theorem, Dependence and Shuffling

Confidence interval for ${θ}/{2}$ in $\text{U}(0, \theta)$

Is there an analytical solution to the distribution of a sum of observations drawn from a Frechet distribution?

Convert units, get different results when fitting extreme value distribution with extRemes

Expectation of the minimum of random variables (Exponential + Erlang)

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