isCOP.RTI {copBasic} | R Documentation |
Is a Copula Right-Tail Increasing
Description
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 is right-tail decreasing for
if and only if for any
,
for almost all . Similarly, a copula
is right-tail decreasing for
if and only if for any
,
for almost all 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, (or
) means that the probability
(or
) is a nondecreasing function of
(or
) for all
(or
).
A positive RTI of either or
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.
Usage
isCOP.RTI(cop=NULL, para=NULL, wrtV=FALSE, delta=0.005, ...)
Arguments
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. |
Value
A logical TRUE
or FALSE
is returned.
Author(s)
W.H. Asquith
References
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.
See Also
Examples
## Not run:
isCOP.RTI(cop=P, delta=0.01) # independence should be FALSE
# but function returns TRUE. Note, 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)