cusp.nc: Calculate the Normalizing Constant of Cobb's Cusp Density In cusp: Cusp-Catastrophe Model Fitting Using Maximum Likelihood

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

 ```1 2 3 4 5``` ```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

`pcusp`, `dcusp`
 `1` ``` cusp:::cusp.nc(2,1) ```