Calculate the Normalizing Constant of Cobb's Cusp Density

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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

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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) 

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 wether 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

Details

The function cusp.nc returns Ψ if mom.order = 0 and Ψ 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.

These functions are not intended to be called directly by the user.

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

Author(s)

Raoul Grasman

See Also

pcusp, dcusp

Examples

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    cusp:::cusp.nc(2,1)