MvInv {BNPdensity}

Invert jump heights function

Description

Determines the jump heights of an increasing additive process by inverting the M(v) function. Use a truncation level based on expected moments of the NGG process (thresholdGG). For internal use.

Usage

MvInv(eps, u = 0.5, alpha = 1, kappa = 1, gama = 1/2, N = 3001)

Arguments

eps

Dummy argument kept for consistency with past versions of the functions

u

Real number. The value of the latent variable at the current step.

alpha

Numeric constant. Total mass of the centering measure.

kappa

Numeric positive constant.

gama

Numeric constant. Discount parameter of the NRMI process.

N

Number of steps in the discretization scheme for the grid inversion.

## The function has been optimised but it is morally defined as: function(eps, u = 0.5, alpha = 1, kappa = 1, gama = 1 / 2, N = 3001) n <- length(w) v <- rep(NA, n) x <- -log(seq(from = exp(-1e-05), to = exp(-10), length = N)) f <- alpha / gamma(1 - gama) * x^(-(1 + gama)) * exp(-(u + kappa) * x) dx <- diff(x) h <- (f[-1] + f[-N]) / 2 Mv <- rep(0, N) for (i in seq(N - 1, 1)) Mv[i] <- Mv[i + 1] + dx[i] * h[i] for (j in seq(n)) v[j] <- x[which.min(Mv > w[j])] return(v)