Calculate the Normalizing Constant of Cobb's Cusp Density

Description Usage Arguments Details Value Author(s) See Also Examples


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 (


5, beta, mom.order = 0, ...), beta, ..., keep.order = TRUE), beta, subdivisions = 100, rel.tol = .Machine$double.eps^0.25, 
    abs.tol = rel.tol, stop.on.error = TRUE, aux = NULL, keep.order = TRUE), beta, ..., keep.order = FALSE) 



the asymmetry parameter in Cobb's cusp density (see cusp)


the bifurcation parameter in Cobb's cusp density (see cusp)


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)


logical, that indicates wether the order of the output should be the same as the order of the input


extra arguments in that are passed to


The function returns Ψ if mom.order = 0 and Ψ times the moment of order mom.order otherwise.

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

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

Value,, return a numeric vector of the same length as alpha and beta with normalizing constants, or the indicated moments times the normalization constant ( only). returns a list with vectors with the results obtained from integrate. first sorts the input in such a way that the numerical integrals can be evaluated more quickly than in arbitrary order


Raoul Grasman

See Also

pcusp, dcusp



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