View source: R/USER_MCmeanvarTMD.R
MCmeanvarTMD | R Documentation |
It computes the Monte Carlo mean vector and variance-covariance matrix for some doubly truncated skew-elliptical distributions. Monte Carlo simulations are performed via slice Sampling.
It supports the p
-variate Normal, Skew-normal (SN), Extended Skew-normal (ESN) and Unified Skew-normal (SUN) as well as the Student's-t, Skew-t (ST), Extended Skew-t (EST) and Unified Skew-t (SUT) distribution.
MCmeanvarTMD(lower = rep(-Inf,length(mu)),upper = rep(Inf,length(mu)),mu,Sigma ,lambda = NULL,tau = NULL,Gamma = NULL,nu = NULL,dist,n = 10000)
lower |
the vector of lower limits of length p. |
upper |
the vector of upper limits of length p. |
mu |
a numeric vector of length p representing the location parameter. |
Sigma |
a numeric positive definite matrix with dimension pxp representing the scale parameter. |
lambda |
a numeric matrix of dimension pxq representing the skewness/shape matrix parameter for the SUN and SUT distribution. For the ESN and EST distributions (q=1), |
tau |
a numeric vector of length q representing the extension parameter for the SUN and SUT distribution. For the ESN and EST distributions, |
Gamma |
a correlation matrix with dimension qxq. It must be provided only for the SUN and SUT cases. For particular cases SN, ESN, ST and EST, we have that |
nu |
It represents the degrees of freedom for the Student's t-distribution being a positive real number. |
dist |
represents the truncated distribution to be used. The values are |
n |
number of Monte Carlo samples to be generated. |
It returns a list with three elements:
mean |
the estimate for the mean vector of length p |
EYY |
the estimate for the second moment matrix of dimensions pxp |
varcov |
the estimate for the variance-covariance matrix of dimensions pxp |
Christian E. Galarza <cgalarza88@gmail.com> and Victor H. Lachos <hlachos@uconn.edu>
Maintainer: Christian E. Galarza <cgalarza88@gmail.com>
Arellano-Valle, R. B. & Genton, M. G. (2005). On fundamental skew distributions. Journal of Multivariate Analysis, 96, 93-116.
Ho, H. J., Lin, T. I., Chen, H. Y., & Wang, W. L. (2012). Some results on the truncated multivariate t distribution. Journal of Statistical Planning and Inference, 142(1), 25-40.
meanvarTMD
, rmvSN
,rmvESN
,rmvST
, rmvEST
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) ## Normal case # Theoretical value value1 = meanvarTMD(a,b,mu,Sigma,dist="normal") #MC estimate MC11 = MCmeanvarTMD(a,b,mu,Sigma,dist="normal") #by defalut n = 10000 MC12 = MCmeanvarTMD(a,b,mu,Sigma,dist="normal",n = 10^5) #more precision ## Skew-t case # Theoretical value value2 = meanvarTMD(a,b,mu,Sigma,lambda = c(-2,0,1),nu = 4,dist = "ST") #MC estimate MC21 = MCmeanvarTMD(a,b,mu,Sigma,lambda = c(-2,0,1),nu = 4,dist = "ST") ## More... MC5 = MCmeanvarTMD(a,b,mu,Sigma,lambda = c(-2,0,1),tau = 1,dist = "ESN") MC6 = MCmeanvarTMD(a,b,mu,Sigma,lambda = c(-2,0,1),tau = 1,nu = 4,dist = "EST") #Skew-unified Normal (SUN) and Skew-unified t (SUT) distributions Lambda = matrix(c(1,0,2,-3,0,-1),3,2) #A skewness matrix p times q Gamma = matrix(c(1,-0.5,-0.5,1),2,2) #A correlation matrix q times q tau = c(-1,2) #A vector of extension parameters of dim q MC7 = MCmeanvarTMD(a,b,mu,Sigma,lambda = Lambda,tau = c(-1,2),Gamma = Gamma,dist = "SUN") MC8 = MCmeanvarTMD(a,b,mu,Sigma,lambda = Lambda,tau = c(-1,2),Gamma = Gamma,nu = 1,dist = "SUT")
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.