# eva: Extreme Value Analysis with Goodness-of-Fit Testing

### Description

The focus of this package is to provide much needed automated diagnostic tools (in the form of statistical hypothesis testing) to extreme value models. Other useful functionality is efficient and user-friendly non-stationary model fitting, profile likelihood confidence intervals, data generation in the r-largest order statistics model (GEVr), and ordered p-value multiplicity adjustments. Also, all routines are implemented to efficiently handle the near-zero shape parameter, which may cause numerical issues in other packages. Functions can be roughly assigned to the following topics:

### Formal (Automated) Goodness-of-Fit Testing

`gevrSeqTests`

is a wrapper function that performs sequential testing
for r in the GEVr distribution, with adjusted p-values. It can implement three
tests:

`gevrEd`

An entropy difference test, which uses an asymptotic normal central limit theorem result.

`gevrPbScore`

A score test, implemented using parametric bootstrap and can be run in parallel.

`gevrMultScore`

An asymptotic approximation to the score test (computationally efficient).

`gpdSeqTests`

is a wrapper function that performs sequential testing
for thresholds in the Generalized Pareto distribution (GPD), with adjusted
p-values. It can implement the following (six) tests:

`gpdAd`

The Anderson-Darling test, with log-linear interpolated p-values. Can also be bootstrapped (with a parallel option).

`gpdCvm`

The Cramer-Von Mises test, with log-linear interpolated p-values. Can also be bootstrapped (with a parallel option).

`gpdImAsym`

An asymptotic information matrix test, with bootstrapped covariance estimates.

`gpdImPb`

A full bootstrap version of information matrix test, with bootstrapped covariance estimates and critical values.

`gpdPbScore`

A score test, implemented using parametric bootstrap and can be run in parallel.

`gpdMultScore`

An asymptotic approximation to the score test (computationally effciient).

`pSeqStop`

A simple function that reads in raw, ordered p-values and returns two sets that adjust
for the familywise error rate and false discovery rate.

### Data generation and model fitting

All the functions in this section (and package) efficiently handle a near-zero value of the shape parameter, which can cause numerical instability in similar functions from other packages. See the vignette for an example.

Data generation, density, quantile, and distribution functions can handle non-stationarity and vectorized inputs.

`gevr`

Data generation and density function for the GEVr distribution,
with distribution function and quantile functions available for GEV1 (block maxima).

`gpd`

Data generation, distribution, quantile, and density functions
for the GPD distribution.

`gevrFit`

Non-stationary fitting of the GEVr distribution, with the option
of maximum product spacings estimation when r=1. Uses formula statements for
user friendliness and automatically centers/scales covariates when appropriate
to speed up optimization.

`gpdFit`

Non-stationary fitting of the GP distribution, with same
options and implementation as ‘gevrFit’. Allows non-stationary
threshold to be used.

`gevrProfShape`

Profile likelihood estimation for the shape
parameter of the stationary GEVr distribution.

`gpdProfShape`

Profile likelihood estimation for the shape
parameter of the stationary GP distribution.

`gevrRl`

Profile likelihood estimation for return levels
of the stationary GEVr distribution.

`gpdRl`

Profile likelihood estimation for return levels
of the stationary GP distribution.

### Visual Diagnostics

`gevrDiag`

, `gpdDiag`

Diagnostic plots for a fit to
the GEVr (GP) distribution. For stationary models, return level, density, quantile,
and probability plots are returned. For non-stationary models, residual quantile,
residual probability, and residuals versus covariate plots are returned.

`mrlPlot`

Plots the empirical mean residual life, with
confidence intervals. Visual diagnostic tool to choose a threshold
for exceedances.

### Data

`fortmax`

Top ten annual precipitation events (inches) for
one rain gauge in Fort Collins, Colorado from 1900 through 1999.

`lowestoft`

Top ten annual sea levels at the LoweStoft station
tide gauge from 1964 - 2014.

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