# ev.trawl v0.1.0

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## Extreme Value Trawls

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) <DOI:10.21314/JEM.2018.179> which can be found on arXiv (<arXiv:1511.08190>) .

## Functions in ev.trawl

Name | Description | |

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

GetEstimateRho | 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. | |

DiffVal | 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. | |

MoMGPD | 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. | |

HessianF | 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). | |

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

GradF | 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. | |

TrawlExp | Returns an exponential trawl function with base time t. | |

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

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

rlexceed | 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. | |

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

TrfG | 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. | |

rtrawl | 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. | |

dlgpd | 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 | Zeta function from auto-correlation expansion for small lags. | |

PairwiseOneZero21 | ||

SecondOrderMixedDiffVal | Second-order bivariate differentiation calculation. | |

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

EvaluateF | Evalutae function at given parameters. | |

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

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

GammaBox | 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. | |

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

ComputeAExp | Wrapper to compute total area under exponential trawl function. | |

ComputeB1Exp | Wrapper to compute difference area between t2 and t1 under exponential trawl function. | |

ComputeB3Exp | Wrapper to compute difference area between t1 and t2 under exponential trawl function. | |

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## Details

Type | Package |

License | MIT + file LICENSE |

Encoding | UTF-8 |

LazyData | true |

RoxygenNote | 6.1.0 |

NeedsCompilation | no |

Packaged | 2018-11-29 15:44:01 UTC; Valentin |

Repository | CRAN |

Date/Publication | 2018-12-03 19:40:08 UTC |

imports | eva , evir , fExtremes , ghyp , hypergeo , stats , testthat |

depends | R (>= 2.10) |

Contributors | Valentin Courgeau |

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