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.
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.
ComputeBInterExp        Wrapper to compute intersection area between
                        't1' and 't2' under exponential trawl function.
DiffVal                 Centered differentiation calculation.
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'.
GammaSqBox              Wrapper for GammaBox using a square to multiply
                        the shape parameter.
GenerateParameters      Computes initial guess for Univariate
                        Latent-Trawl model. Uses 'fExtreme' package
                        method 'gpdFit' to fit MLE.
GetEstimateRho          Computes first-order estimate for 'rho'.
GradF                   Computes gradident of a function given
                        parameters and offset value epsilon.
HessianF                Computes Hessian matrix of a $C^2$ function
                        given parameters and offset value epsilon
MarginalGPDLikelihood   Computes Generalised Pareto (log-)likelihood on
                        non-zero exceedances under independence.
MarginalSimpleLik       Simplified marginal (GPD) log-likelihood
                        function under independence in the exponential
                        trawl case.
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.
PairwiseOneOne          Computes latent trawl pairwise likelihood with
                        '(x,x)' where 'x' and 'y' positive with
                        exponential trawl function.
PairwiseOneOne1         Computes first term in latent trawl pairwise
                        likelihood with '(x,x)' where 'x' positive and
                        'y' positive.
PairwiseOneOne11        Computes frst part of first term in latent
                        trawl pairwise likelihood with '(x,x)' where
                        'x' positive and 'y' positive.
PairwiseOneOne12        Computes second part of first 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.
PairwiseOneOne2         Computes second term in latent trawl pairwise
                        likelihood with '(x,x)' where 'x' positive and
                        'y' positive.
PairwiseOneOne21        Computes second term in latent trawl pairwise
                        likelihood with '(x,x)' where 'x' positive and
                        'y' positive.
PairwiseOneOne22        Computes second term in latent trawl pairwise
                        likelihood with '(x,x)' where 'x' positive and
                        'y' positive.
PairwiseOneOne23        Computes second term in latent trawl pairwise
                        likelihood with '(x,x)' where 'x' positive and
                        'y' positive.
PairwiseOneOne24        Computes second term in latent trawl pairwise
                        likelihood with '(x,x)' where 'x' positive and
                        'y' positive.
PairwiseOneZero         Computes term in latent trawl pairwise
                        likelihood with '(x,0)' where 'x' positive with
                        exponential trawl function.
PairwiseOneZero1        Computes first part of latent trawl pairwise
                        likelihood with '(x,0)' where 'x' positive.
PairwiseOneZero2        Computes second term in latent trawl pairwise
                        likelihood with '(x,0)' where 'x' positive.
PairwiseOneZero21       Computes partial part of second term in latent
                        trawl pairwise likelihood with '(x,0)' where
                        'x' positive.
PairwiseOneZero22       Computes partial part of second term in latent
                        trawl pairwise likelihood with '(x,0)' where
                        'x' positive.
PairwiseOneZero23       Computes partial part of second term in latent
                        trawl pairwise likelihood with '(x,0)' where
                        'x' positive.
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.
PairwiseZeroZero1       Computes partial part of latent trawl pairwise
                        likelihood with '(x,y) = (0,0)'.
PairwiseZeroZero2       Computes second part of latent trawl pairwise
                        likelihood with '(x,y) = (0,0)'.
ParamsListFullPL        Wrapper for FullPL using a list for parameters
                        in the exponential trawl case.
SecondOrderDiffVal      Second-order centered differentiation
                        calculation.
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.
SliceArea               Computes the area of a slice for the Slice
                        Partition method of trawl functions.
TrawlExp                Returns an exponential trawl function with base
                        time t.
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.
TrfFindOffsetScale      Computes predefined transformed scale
                        parameter.
TrfG                    Computes g from the marginal transform method
                        (vectorised version). That is from GPD(alpha,
                        beta+kappa) to GPD(offset_shape, offset_scale).
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).
TrfJacobian             Computes determinant of Jacobian of Marginal
                        Transform (MT) method.
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.
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.
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'.
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.
