trunmnt (version 1.0.0)

prodmnt: Compute the product moment.

Description

It computes the kappa-th order product moment for a truncated multivariate normal distribution.

Usage

prodmnt(Obj, kappa)

Value

a numeric value.

Arguments

Obj

mtrunmnt object created by the mtrunmnt.

kappa

Vector of orders of length equal to mu.

Details

prodmnt is a S3 generic function of the class mtrunmnt. Using the multivariate Gaussian quadrature, it computes the product moment \(E(\prod_{i=1}^n Y_i^{k_i}) | a_i < Y_i < b_i, i = 1, \ldots, n)\), where \(Y \sim N(\mu, ZDZ' + E)\).

See Also

mtrunmnt, momentsTMD.

Examples

###  A simple example ####

set.seed(123)
sigma2e <- 1
sigma2a <- 2
n <- 5
mu <- seq(-1,1, length.out = n)
y <- mu + rnorm(1, sd = sqrt(sigma2a)) + rnorm(n, sd = sqrt(sigma2e))
a  <- rep(-Inf, n)
b  <- rep(Inf, n)
a[y >= 0] <- 0
b[y <  0] <- 0
obj <- mtrunmnt(mu, lower = a, upper = b, Sigmae = sigma2e, D = sigma2a) 
prodmnt(obj, c(2,2,0,0,0))