Description Usage Arguments Value Author(s) Examples

A collection and description of functions to investigate
bivariate elliptical copulae.

Elliptical Copulae Functions:

`ellipticalCopulaSim` | simulates an elliptical copula, |

`ellipticalCopulaFit` | fits the parameters of an elliptical copula. |

1 2 3 | ```
ellipticalCopulaSim(n, rho = 0.75, param = NULL, type = c("norm", "cauchy", "t"))
ellipticalCopulaFit(u, v, type = c("norm", "cauchy", "t"), ...)
``` |

`n` |
[rellipticalCopula][ellipticalCopulaSim] - |

`rho` |
[*ellipticalCopula] - |

`param` |
[*ellipticalCopula][gfunc] - |

`type` |
[*ellipticalCopula][gfunc] - |

`u, v` |
[*ellipticalCopula] - |

`...` |
[ellipticalCopulaFit] - |

**Copula Functions:**

The functions `[rpd]ellipticalCopula`

return a numeric vector
of random variates, probabilities, or densities for the specified
copula computed at grid coordinates `u`

|`v`

.

The functions `[rpd]ellipticalSlider`

display an interactive
graph of an perspective copula plot either for random variates,
probabilities or densities. Alternatively, an image underlayed
contour plot can be shown.

**Copula Dependence Measures:**

The functions `ellipticalTau`

and `ellipticalRho`

return
a numericc value for Kendall's Tau and Spearman's Rho.

**Copula Tail Coefficient:**

The function `ellipticalTailCoeff`

returns the coefficient of
tail dependence for a specified copula. The function
`ellipticalTailPlot`

displays a whole plot for the upper or
alternatively for the lower tail dependence as a function of
`u`

for a set of nine `rho`

values.

**Copula Generator Function:**

The function `gfunc`

computes the generator function for the
specified copula, by default the normal copula. If the argument
`x`

is missing, then the normalization constand lambda will
be returned, otherwise if `x`

is specified the values for the
function *g(x)* will be freturned. The selected type of copula
is added to the output as an attribute named `"control"`

.
The function `gfuncSlider`

allows to display interactively
the generator function, the marginal density, the marginal
probability, and the contours of the the bivariate density.

**Copula Simulation and Parameter Fitting:**

The function `ellipticalCopulaSim`

returns a numeric two-column
matrix with randomly generated variates for the specified copula.

The function `ellipticalCopulaFit`

returns a fit to empirical
data for the specified copula. The returned object is a list with
elements from the function `nlminb`

.

Diethelm Wuertz for the Rmetrics **R**-port.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 | ```
## [rp]ellipticalCopula -
# Default Normal Copula:
rellipticalCopula(10)
pellipticalCopula(10)
## [rp]ellipticalCopula -
# Student-t Copula Probability and Density:
u = grid2d(x = (0:25)/25)
# CHECK ERROR
# pellipticalCopula(u, rho = 0.75, param = 4,
# type = "t", output = "list")
# CHECK ERROR DONE
d = dellipticalCopula(u, rho = 0.75, param = 4,
type = "t", output = "list")
persp(d, theta = -40, phi = 30, col = "steelblue")
## ellipticalTau -
## ellipticalRho -
# Dependence Measures:
ellipticalTau(rho = -0.5)
ellipticalRho(rho = 0.75, type = "logistic", subdivisions = 100)
## ellipticalTailCoeff -
# Student-t Tail Coefficient:
ellipticalTailCoeff(rho = 0.25, param = 3, type = "t")
## gfunc -
# Generator Function:
plot(gfunc(x = 0:10), main = "Generator Function")
## ellipticalCopulaSim -
## ellipticalCopulaSim -
# Simualtion and Parameter Fitting:
rv <- ellipticalCopulaSim(n = 100, rho = 0.75)
ellipticalCopulaFit(rv)
``` |

fCopulae documentation built on Nov. 17, 2017, 2:31 p.m.

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