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ev.trawl (version 0.1.0)

Extreme Value Trawls

Description

Implementation of trawl processes and an extension of such processes into a univariate latent model for extreme values. Inference, simulation and initialization tools are available. See Noven et al. (2018) which can be found on arXiv () .

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Install

install.packages('ev.trawl')

Monthly Downloads

2

Version

0.1.0

License

MIT + file LICENSE

Maintainer

Valentin Courgeau

Last Published

December 3rd, 2018

Functions in ev.trawl (0.1.0)

Computes latent trawl pairwise likelihood with (x,x) where x and y positive with exponential trawl function.

Computes first-order estimate for rho.

MarginalSimpleLik

Simplified marginal (GPD) log-likelihood function under independence in the exponential trawl case.

PairwiseOneZero

Computes term in latent trawl pairwise likelihood with (x,0) where x positive with exponential trawl function.

Centered differentiation calculation.

ComputeBInterExp

Wrapper to compute intersection area between t1 and t2 under exponential trawl function.

PairwiseOneZero1

Computes first part of latent trawl pairwise likelihood with (x,0) where x positive.

Method of moments (MoM) on a one or multiple exceedance timeseries for the latent trawl model using marginal GPD properties and probability of exceedance.

SecondOrderDiffVal

Second-order centered differentiation calculation.

ParamsListFullPL

Wrapper for FullPL using a list for parameters in the exponential trawl case.

Computes Hessian matrix of a $C^2$ function given parameters and offset value epsilon

PairwiseOneOne1

Computes first term in latent trawl pairwise likelihood with (x,x) where x positive and y positive.

PairwiseZeroZero1

Computes partial part of latent trawl pairwise likelihood with (x,y) = (0,0).

Computes inverse of g from the marginal transform method (vectorised version). That is from GPD(offset_shape, offset_scale) to GPD(alpha, beta+kappa).

Computes gradident of a function given parameters and offset value epsilon.

PairwiseOneOne2

Computes second term in latent trawl pairwise likelihood with (x,x) where x positive and y positive.

PairwiseOneOne13

Computes third part of first term in latent trawl pairwise likelihood with (x,x) where x positive and y positive.

PairwiseZeroZero2

Computes second part of latent trawl pairwise likelihood with (x,y) = (0,0).

PairwiseOneOne21

Computes second term in latent trawl pairwise likelihood with (x,x) where x positive and y positive.

GenerateParameters

Computes initial guess for Univariate Latent-Trawl model. Uses fExtreme package method gpdFit to fit MLE.

PairwiseOneOne23

Computes second term in latent trawl pairwise likelihood with (x,x) where x positive and y positive.

MarginalGPDLikelihood

Computes Generalised Pareto (log-)likelihood on non-zero exceedances under independence.

PairwiseOneZero24

Computes partial part of second term in latent trawl pairwise likelihood with (x,0) where x positive.

PairwiseZeroZero

Computes latent trawl pairwise likelihood with (x,y) = (0,0) for Exponential Trawl funciton.

Returns an exponential trawl function with base time t.

Computes the area of a slice for the Slice Partition method of trawl functions.

Computes the cumulative distribution function of Generalised Pareto Distribution at x, with shape parameter alpha and scale parameter beta.

Simulation of extreme value path using latent trawl process. Transformed marginals have scale parameter 1+kappa.

PairwiseOneOne11

Computes frst part of first term in latent trawl pairwise likelihood with (x,x) where x positive and y positive.

TrfFindOffsetScale

Computes predefined transformed scale parameter.

PairwiseOneOne12

Computes second part of first term in latent trawl pairwise likelihood with (x,x) where x positive and y positive.

Computes determinant of Jacobian of Marginal Transform (MT) method.

Computes g from the marginal transform method (vectorised version). That is from GPD(alpha, beta+kappa) to GPD(offset_shape, offset_scale).

PairwiseOneOne22

Computes second term in latent trawl pairwise likelihood with (x,x) where x positive and y positive.

PairwiseOneZero22

Computes partial part of second term in latent trawl pairwise likelihood with (x,0) where x positive.

PairwiseOneOne24

Computes second term in latent trawl pairwise likelihood with (x,x) where x positive and y positive.

Simulation of trawl process path using Slice partition. If using customised trawl functions and primitives (i.e. trawl.function = NA), then, it is required that the user provides length(times) + deep_cols such functions and primitives where the deep_cols first one are used to reconstuct the first trawl value.

Computes the probability density function of Generalised Pareto Distribution at x, with shape parameter alpha and scale parameter beta.

hourly_bloomsbury_air_pollution_2000_2017

Hourly measurements of 6 air pollutant concentrations in Bloomsbury, London, UK.

PairwiseOneZero23

Computes partial part of second term in latent trawl pairwise likelihood with (x,0) where x positive.

TrawlExpPrimitive

Returns a primitive of exponential trawl function with base time t. Such primitive has its zero at zero_at.

TrawlSliceReconstruct

Performs trawl slices reconstuction to get gamma samples using the independent measure scaterring.

PairwiseOneZero2

Computes second term in latent trawl pairwise likelihood with (x,0) where x positive.

UnivariateFullPL

Computes univariate latent trawl FULL pairwise likelihood depending with exponential trawl function with the option to fix some parameter values.

Zeta function from auto-correlation expansion for small lags.

PairwiseOneZero21

Computes partial part of second term in latent trawl pairwise likelihood with (x,0) where x positive.

SecondOrderMixedDiffVal

Second-order bivariate differentiation calculation.

Computes correct latent trawl SINGLE pairwise likelihood depending on the values of (x1,x2) with exponential trawl function.

Evalutae function at given parameters.

Computes latent trawl FULL pairwise likelihood depending with exponential trawl function.

Generalised Pareto likelihood maximisation using L-BFGS-B optimisation routine.

Sample Gamma with small shape parameter alpha*dx*dy.

CollectionTrawl

Creates a list of trawl functions given a type of trawl and a vector of times as peak times. Has the option to get primitives. Note that only exponential trawl are implemented so far.

Wrapper for GammaBox using a square to multiply the shape parameter.

Wrapper to compute total area under exponential trawl function.

Wrapper to compute difference area between t2 and t1 under exponential trawl function.

Wrapper to compute difference area between t1 and t2 under exponential trawl function.