MomTrunc (version 6.0)

MomTrunc-package: MomTrunc

Description

MomTrunc

Details

Probabilities can be computed using the functions pmvSN and pmvESN for the normal cases SN and ESN and, pmvST and pmvEST for the t cases ST and EST respectively, which offer the option to return the logarithm in base 2 of the probability, useful when the true probability is too small for the machine precision. These functions above use methods in Genz (1992) through the mvtnorm package (linked direclty to our C++ functions) and Cao et.al. (2019) through the package tlrmvnmvt. For the double truncated Student-t cases SUT, EST, ST and T, decimal degrees of freedom are supported. Computation of arbitrary moments are based in the works of Kan & Robotti (2017) and Galarza et.al. (2021,2022a,2022b). Reference for the family of selection-elliptical distributions in this package can be found in Arellano-Valle & Genton (2005).

References

Arellano-Valle, R. B. & Genton, M. G. (2005). On fundamental skew distributions. Journal of Multivariate Analysis, 96, 93-116.

Cao, J., Genton, M. G., Keyes, D. E., & Turkiyyah, G. M. (2019) "Exploiting Low Rank Covariance Structures for Computing High-Dimensional Normal and Student-t Probabilities" <https://marcgenton.github.io/2019.CGKT.manuscript.pdf>.

Galarza, C. E., Lin, T. I., Wang, W. L., & Lachos, V. H. (2021). On moments of folded and truncated multivariate Student-t distributions based on recurrence relations. Metrika, 84(6), 825-850 <doi:10.1007/s00184-020-00802-1>.

Galarza, C. E., Matos, L. A., Dey, D. K., & Lachos, V. H. (2022a). "On moments of folded and doubly truncated multivariate extended skew-normal distributions." Journal of Computational and Graphical Statistics, 1-11 <doi:10.1080/10618600.2021.2000869>.

Galarza, C. E., Matos, L. A., Castro, L. M., & Lachos, V. H. (2022b). Moments of the doubly truncated selection elliptical distributions with emphasis on the unified multivariate skew-t distribution. Journal of Multivariate Analysis, 189, 104944 <doi:10.1016/j.jmva.2021.104944>.

Genz, A., "Numerical computation of multivariate normal probabilities," Journal of Computational and Graphical Statistics, 1, 141-149 (1992) <doi:10.1080/10618600.1992.10477010>.

Kan, R., & Robotti, C. (2017). On moments of folded and truncated multivariate normal distributions. Journal of Computational and Graphical Statistics, 26(4), 930-934.

See Also

onlymeanTMD,meanvarTMD,momentsTMD,dmvSN,pmvSN,rmvSN,dmvST,pmvST,rmvST

Examples

# NOT RUN {
a = c(-0.8,-0.7,-0.6)
b = c(0.5,0.6,0.7)
mu = c(0.1,0.2,0.3)
Sigma = matrix(data = c(1,0.2,0.3,0.2,1,0.4,0.3,0.4,1),
               nrow = length(mu),ncol = length(mu),byrow = TRUE)

meanvarTMD(a,b,mu,Sigma,dist="normal") #normal case
meanvarTMD(mu = mu,Sigma = Sigma,lambda = c(-2,0,1),dist="SN") #skew normal with NO truncation
meanvarTMD(a,b,mu,Sigma,lambda = c(-2,0,1),nu = 4.87,dist = "ST") #skew t
momentsTMD(3,a,b,mu,Sigma,nu = 4,dist = "t") #t case, all moments or order <=3
# }