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 Computes partial part of second term in latent trawl pairwise likelihood with (x,0) where x positive. 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. No Results!