pcmvtruncnorm {condTruncMVN}

CDF for the Conditional Truncated Multivariate Normal

Description

Computes the distribution function for a conditional truncated multivariate normal random variate Y|X.

Usage

pcmvtruncnorm(
  lowerY,
  upperY,
  mean,
  sigma,
  lower,
  upper,
  dependent.ind,
  given.ind,
  X.given,
  ...
)

Arguments

lowerY

the vector of lower limits for Y|X. Passed to tmvtnorm::ptmvnorm().

upperY

the vector of upper limits for Y|X. Must be greater than lowerY. Passed to tmvtnorm::ptmvnorm().

mean

the mean vector for Z of length of n

sigma

the symmetric and positive-definite covariance matrix of dimension n x n of Z.

lower

a vector of lower bounds of length n that truncate Z

upper

a vector of upper bounds of length n that truncate Z

dependent.ind

a vector of integers denoting the indices of dependent variable Y.

given.ind

a vector of integers denoting the indices of conditioning variable X. If specified as integer vector of length zero or left unspecified, the unconditional density is returned.

X.given

a vector of reals denoting the conditioning value of X. This should be of the same length as given.ind

...

Additional arguments passed to tmvtnorm::ptmvnorm(). The CDF is calculated using the Genz algorithm based on these arguments: maxpts, abseps, and releps.

Details

Calculates the probability that Y|X is between lowerY and upperY. Z = (X, Y) is the fully joint multivariate normal distribution with mean equal mean and covariance matrix sigma, truncated between lower and upper. See the vignette for more information.

Note

For one-dimension conditionals Y|X, this function uses the ptruncnorm() function in the truncnorm package. Otherwise, this function uses tmvtnorm::ptmvnorm().

Examples

# Example 1: Let X2,X3,X5|X2,X4 ~ N_3(1, Sigma)
# truncated between -10 and 10.
d <- 5
rho <- 0.9
Sigma <- matrix(0, nrow = d, ncol = d)
Sigma <- rho^abs(row(Sigma) - col(Sigma))

# Find P(-0.5 < X2,X3,X5 < 0 | X2,X4)
pcmvtruncnorm(rep(-0.5, 3), rep(0, 3),
  mean = rep(1, d),
  sigma = Sigma,
  lower = rep(-10, d),
  upper = rep(10, d),
  dependent.ind = c(2, 3, 5),
  given.ind = c(1, 4), X.given = c(1, -1)
)

# Example 2: Let X1| X2 = 1, X3 = -1, X4 = 1, X5 = -1 ~ N(1, Sigma) truncated
# between -10 and 10. Find P(-0.5 < X1 < 0 | X2 = 1, X3 = -1, X4 = 1, X5 = -1).
pcmvtruncnorm(-0.5, 0,
  mean = rep(1, d),
  sigma = Sigma,
  lower = rep(-10, d),
  upper = rep(10, d),
  dependent.ind = 1,
  given.ind = 2:5, X.given = c(1, -1, 1, -1)
)