Computes latent trawl pairwise likelihood with (x,x) where x
and y positive with exponential trawl function.
Computes first-order estimate for rho.
Simplified marginal (GPD) log-likelihood function under independence in the
exponential trawl case.
Computes term in latent trawl pairwise likelihood with (x,0) where x positive
with exponential trawl function.
Centered differentiation calculation.
Wrapper to compute intersection area between t1 and t2
under exponential trawl function.
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.
Second-order centered differentiation calculation.
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
Computes first term in latent trawl pairwise likelihood with (x,x) where x positive and y positive.
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.
Computes second term in latent trawl pairwise likelihood with (x,x)
where x positive and y positive.
Computes third part of first term in latent trawl pairwise likelihood with (x,x) where x positive and y positive.
Computes second part of latent trawl pairwise likelihood with (x,y) = (0,0).
Computes second term in latent trawl pairwise likelihood with (x,x)
where x positive and y positive.
Computes initial guess for Univariate Latent-Trawl model.
Uses fExtreme package method gpdFit to fit MLE.
Computes second term in latent trawl pairwise likelihood with (x,x)
where x positive and y positive.
Computes Generalised Pareto (log-)likelihood on non-zero exceedances under
independence.
Computes partial part of second term in latent trawl pairwise likelihood with (x,0) where x positive.
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.
Computes frst part of first term in latent trawl pairwise likelihood with (x,x) where x positive and y positive.
Computes predefined transformed scale parameter.
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).
Computes second term in latent trawl pairwise likelihood with (x,x)
where x positive and y positive.
Computes partial part of second term in latent trawl pairwise likelihood with (x,0) where x positive.
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.
Computes partial part of second term in latent trawl pairwise likelihood with (x,0) where x positive.
Returns a primitive of exponential trawl function with base time t. Such
primitive has its zero at zero_at.
Performs trawl slices reconstuction to get gamma samples using the
independent measure scaterring.
Computes second term in latent trawl pairwise likelihood with (x,0)
where x positive.
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.
Computes partial part of second term in latent trawl pairwise likelihood with (x,0) where x positive.
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.
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.