MTCE: Multivariate tail conditional expectation

In MultiStatM: Multivariate Statistical Methods

Multivariate tail conditional expectation

Description

It provides the conditional expectation

\text{MTCE}_q(\mathbf{X}) = \operatorname{E} \left( \mathbf{X} \mid X_1 > \text{VaR}_q (X_1), X_2 > \text{VaR}_q (X_2), \dots, X_n > \text{VaR}_q (X_d) \right),

for q \in (0,1), where \text{VaR}_q(X) is the q-th quantile of the random variable X. Expectation is taken with respect to GramCharlier with the first 4 cumulants.

Usage

MTCE(X, cum)

Arguments

X	a vector of unstandardized VaRq
cum	list of mean, variance, skewness and kurtosis vectors

Details

For further details see the references below,

Value

Numerator of the ratio

Denominator of the ratio

MTCE Conditional expected value

References

Landsman, Z., Makov, U., & Shushi, T. (2016). Multivariate tail conditional expectation for elliptical distributions. Insurance: Mathematics and Economics, 70, 216-223.

See Also

Other Approximations: Edgeworth(), GramCharlier(), IntEdgeworth(), IntGramCharlier()

Examples

x <- c(2,3,4)
cum <- MomCumMVt(p = 12, d = 3, r = 4, nCum = TRUE)
CE <- MTCE(x, cum)

MultiStatM documentation built on Jan. 25, 2026, 5:06 p.m.