# 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

1 2 3 4 5 |

### Arguments

`alpha` |
the asymmetry parameter in Cobb's cusp density (see |

`beta` |
the bifurcation parameter in Cobb's cusp density (see |

`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 |

`keep.order` |
logical, that indicates wether the order of the output should be the same as the order of the input |

`...` |
extra arguments in |

### 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

1 |

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