cusp.nc: Calculate the Normalizing Constant of Cobb's Cusp Density

Description

A family of functions that return the normalization constant for the cusp density given the values of the bifurcation and asymmetry parameters (default), or returns the moment of a specified order (cusp.nc).

Usage

cusp.nc(alpha, beta, mom.order = 0, ...)
cusp.nc.c(alpha, beta, ..., keep.order = TRUE) 
cusp.nc.C(alpha, beta, subdivisions = 100, rel.tol = .Machine$double.eps^0.25, 
    abs.tol = rel.tol, stop.on.error = TRUE, aux = NULL, keep.order = TRUE) 
cusp.nc.vec(alpha, beta, ..., keep.order = FALSE)

Value

cusp.nc, cusp.nc.c, cusp.nc.vec return a numeric vector of the same length as alpha and beta with normalizing constants, or the indicated moments times the normalization constant (cusp.nc only).

cusp.nc.C returns a list with vectors with the results obtained from integrate.

cusp.nc.c first sorts the input in such a way that the numerical integrals can be evaluated more quickly than in arbitrary order

Arguments

alpha: the asymmetry parameter in Cobb's cusp density (see cusp)
beta: the bifurcation parameter in Cobb's cusp density (see cusp)
mom.order: the moment order to be computed (see details below)
subdivisions, rel.tol, abs.tol, stop.on.error, aux: Arguments used by the internal integration routine of R (see integrate).
keep.order: Logical, that indicates whether the order of the output should be the same as the order of the input.
...: Extra arguments in cusp.nc.c that are passed to cusp.nc.C.

Author

Raoul Grasman

Details

The function cusp.nc returns \(\Psi\) if mom.order = 0 and \(\Psi\) times the moment of order mom.order otherwise.

The function cusp.nc is internally used if the C-routine symbol "cuspnc" is not loaded. The functions cusp.nc.c and cusp.nc.C call this C routine, which is considerably faster than cusp.nc.