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

Numerically set a logical whether a copula is *right-tail increasing* (RTI) as described by Nelsen (2006, pp. 192–193) and Salvadori *et al.* (2007, p. 222). A copula *\mathbf{C}(u,v)* is right-tail decreasing for *\mathrm{RTI}(V{\mid}U)* if and only if for any *v \in [0,1]*,

*\frac{δ \mathbf{C}(u,v)}{δ u} ≤ \frac{v - \mathbf{C}(u,v)}{1 - u}*

for almost all *u \in [0,1]*. Similarly, a copula *\mathbf{C}(u,v)* is right-tail decreasing for *\mathrm{RTI}(U{\mid}V)* if and only if for any *u \in [0,1]*,

*\frac{δ \mathbf{C}(u,v)}{δ v} ≤ \frac{u - \mathbf{C}(u,v)}{1 - v}*

for almost all *v \in [0,1]* where the later definition is controlled by the `wrtV=TRUE`

argument.

The RTI concept is associated with the concept of *tail monotonicity* (Nelsen, 2006, p. 191). Specifically, but reference to Nelsen (2006) definitions and geometric interpretations is recommended, *\mathrm{RTI}(V{\mid}U)* (or *\mathrm{RTI}(V{\mid}U)*) means that the probability *P[Y > y|X > x]* (or *P[X > x|Y > y]*) is a nondecreasing function of *x* (or *y*) for all *y* (or *x*).

A positive RTI of either *\mathrm{RTI}(V{\mid}U)* or *\mathrm{RTI}(U{\mid}V)* implies positively quadrant dependency (PQD, `isCOP.PQD`

) but the condition of PQD does not imply RTI. Finally, the accuracy of the numerical assessment of the returned logical by `isCOP.RTI`

is dependent on the the smallness of the `delta`

argument passed into the function.

1 |

`cop` |
A copula function; |

`para` |
Vector of parameters, if needed, to pass to the copula; |

`wrtV` |
A logical to toggle between with respect to |

`delta` |
The increment of |

`...` |
Additional arguments to pass to the copula or derivative of a copula function. |

A logical `TRUE`

or `FALSE`

is returned.

W.H. Asquith

Nelsen, R.B., 2006, An introduction to copulas: New York, Springer, 269 p.

Salvadori, G., De Michele, C., Kottegoda, N.T., and Rosso, R., 2007, Extremes in nature—An approach using copulas: Dordrecht, Netherlands, Springer, Water Science and Technology Library 56, 292 p.

1 2 3 4 5 6 7 8 9 | ```
## Not run:
isCOP.RTI(cop=P, delta=0.01) # independence should be FALSE
# but function returns TRUE, note that same logic for isCOP.LTD returns FALSE.
isCOP.RTI(cop=PSP) # TRUE : positive assoc.
isCOP.RTI(cop=PLACKETTcop, para=.15) # FALSE : negative assoc. Plackett
isCOP.RTI(cop=PLACKETTcop, para=15) # TRUE : positive assoc. Plackett
isCOP.RTI(cop=PLACKETTcop, wrtv=TRUE, para=.15) # FALSE : negative assoc. Plackett
isCOP.RTI(cop=PLACKETTcop, wrtV=TRUE, para=15) # TRUE : positive assoc. Plackett
## End(Not run)
``` |

wasquith/copBasic documentation built on Nov. 20, 2019, 5:12 a.m.

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