isCOP.LTD {copBasic} | R Documentation |
Is a Copula Left-Tail Decreasing
Description
Numerically set a logical whether a copula is left-tail decreasing (LTD) as described by Nelsen (2006, pp. 192–193) and Salvadori et al. (2007, p. 222). A copula is left-tail decreasing for
if and only if for any
that the following holds
for almost all . Similarly, a copula
is left-tail decreasing for
if and only if for any
that the following holds
for almost all where the later definition is controlled by the
wrtV=TRUE
argument.
The LTD 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 nonincreasing function of
(or
) for all
(or
).
A positive LTD of either or
implies positively quadrant dependency (PQD,
isCOP.PQD
) but the condition of PQD does not imply LTD. Finally, the accuracy of the numerical assessment of the returned logical by isCOP.LTD
is dependent on the the “smallness” of the delta
argument passed into the function.
Usage
isCOP.LTD(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.LTD(cop=P, delta=0.01) # independence should be FALSE
# Positive association
isCOP.LTD(cop=PSP) # TRUE
# Negative association Plackett
isCOP.LTD(cop=PLACKETTcop, para=0.15) # FALSE
# Positive association Plackett
isCOP.LTD(cop=PLACKETTcop, para=15) # TRUE
# Negative association Plackett
isCOP.LTD(cop=PLACKETTcop, wrtv=TRUE, para=0.15) # FALSE
# Positive association Plackett
isCOP.LTD(cop=PLACKETTcop, wrtV=TRUE, para=15) # TRUE
## End(Not run)