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https://github.com/paulnorthrop/exdex
Estimation of the Extremal Index
https://github.com/paulnorthrop/exdex
block-maxima extremal-index extreme extreme-value-statistics extremes inference maxima semiparametric semiparametric-estimation semiparametric-maxima-estimators theta threshold value
Last synced: 9 days ago
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Estimation of the Extremal Index
- Host: GitHub
- URL: https://github.com/paulnorthrop/exdex
- Owner: paulnorthrop
- Created: 2019-02-17T19:52:26.000Z (almost 6 years ago)
- Default Branch: master
- Last Pushed: 2024-04-27T18:31:49.000Z (8 months ago)
- Last Synced: 2024-12-08T02:08:52.302Z (26 days ago)
- Topics: block-maxima, extremal-index, extreme, extreme-value-statistics, extremes, inference, maxima, semiparametric, semiparametric-estimation, semiparametric-maxima-estimators, theta, threshold, value
- Language: R
- Homepage: https://paulnorthrop.github.io/exdex/
- Size: 9.53 MB
- Stars: 0
- Watchers: 1
- Forks: 1
- Open Issues: 0
-
Metadata Files:
- Readme: README.Rmd
Awesome Lists containing this project
README
---
output: github_document
---
```{r, echo = FALSE}
knitr::opts_chunk$set(
collapse = TRUE,
comment = "#>",
fig.path = "README-"
)
```
# exdex
[](https://ci.appveyor.com/project/paulnorthrop/exdex)
[](https://github.com/paulnorthrop/exdex/actions/workflows/R-CMD-check.yaml)
[](https://app.codecov.io/github/paulnorthrop/exdex?branch=master)
[](https://cran.r-project.org/package=exdex)
[](https://cran.r-project.org/package=exdex)
[](https://cran.r-project.org/package=exdex)
## Estimation of the Extremal Index
### What does exdex do?
The extremal index $\theta$ is a measure of the degree of local dependence in the extremes of a stationary process. The `exdex` package performs frequentist inference about $\theta$ using two types of methodology.
One type ([Northrop, 2015](https://doi.org/10.1007/s10687-015-0221-5)) is based on a model that relates the distribution of block maxima to the marginal distribution of the data, leading to a semiparametric maxima estimator. Two versions of this type of estimator are provided, following [Northrop, 2015](https://doi.org/10.1007/s10687-015-0221-5) and [Berghaus and Bücher, 2018](https://doi.org/10.1214/17-AOS1621). A slightly modified version of the latter is also provided. Estimates are produced using both disjoint and sliding block maxima, the latter providing greater precision of estimation. A graphical block size diagnostic is provided.
The other type of methodology uses a model for the distribution of threshold inter-exceedance times ([Ferro and Segers, 2003](https://doi.org/10.1111/1467-9868.00401)). Three versions of this type of approach are provided: the iterated weight least squares approach of [Süveges (2007)](https://doi.org/10.1007/s10687-007-0034-2), the $K$-gaps model of [Süveges and Davison (2010)](https://doi.org/10.1214/09-AOAS292) and a similar approach of [Holesovsky and Fusek (2020)](https://doi.org/10.1007/s10687-020-00374-3) that we refer to as D-gaps. For the $K$-gaps and $D$-gaps models the `exdex` package allows missing values in the data, can accommodate independent subsets of data, such as monthly or seasonal time series from different years, and can incorporate information from censored inter-exceedance times. Graphical diagnostics for the threshold level and the respective tuning parameters $K$ and $D$ are provided.
### A simple example
The following code estimates the extremal index using the semiparametric maxima estimators, for an example dataset containing a time series of sea surges measured at Newlyn, Cornwall, UK over the period 1971-1976. The block size of 20 was chosen using a graphical diagnostic provided by `choose_b()`.
```{r}
library(exdex)
theta <- spm(newlyn, 20)
theta
summary(theta)
```
Now we estimate $\theta$ using the $K$-gaps model. The threshold $u$ and runs parameter $K$ were chosen using the graphical diagnostic provided by `choose_uk()`.
```{r}
u <- quantile(newlyn, probs = 0.60)
theta <- kgaps(newlyn, u, k = 2)
theta
summary(theta)
```
### Installation
To get the current released version from CRAN:
```{r installation, eval = FALSE}
install.packages("exdex")
```
### Vignette
See `vignette("exdex-vignette", package = "exdex")` for an overview of the package.