ptmvt {tmvtnorm}

Truncated Multivariate Student t Distribution

Description

Computes the distribution function of the truncated multivariate t distribution

Usage

ptmvt(lowerx, upperx, mean = rep(0, length(lowerx)), sigma, df = 1, 
  lower = rep(-Inf, length = length(mean)), 
  upper = rep(Inf, length = length(mean)), maxpts = 25000, abseps = 0.001, 
  releps = 0)

Arguments

lowerx

the vector of lower limits of length n.

upperx

the vector of upper limits of length n.

mean

the mean vector of length n.

sigma

the covariance matrix of dimension n. Either corr or sigma can be specified. If sigma is given, the problem is standardized. If neither corr nor sigma is given, the identity matrix is used for sigma.

df

Degrees of freedom parameter

lower

Vector of lower truncation points, default is rep(-Inf, length = length(mean)).

upper

Vector of upper truncation points, default is rep( Inf, length = length(mean)).

maxpts

maximum number of function values as integer.

abseps

absolute error tolerance as double.

releps

relative error tolerance as double.

Value

The evaluated distribution function is returned with attributes

error

estimated absolute error and

msg

status messages.

Author(s)

Stefan Wilhelm <[e-mail]>

References

Geweke, J. F. (1991) Efficient simulation from the multivariate normal and Student-t distributions subject to linear constraints and the evaluation of constraint probabilities. https://www.researchgate.net/publication/2335219_Efficient_Simulation_from_the_Multivariate_Normal_and_Student-t_Distributions_Subject_to_Linear_Constraints_and_the_Evaluation_of_Constraint_Probabilities

Samuel Kotz, Saralees Nadarajah (2004). Multivariate t Distributions and Their Applications. Cambridge University Press

Examples

sigma <- matrix(c(5, 0.8, 0.8, 1), 2, 2)
Fx <- ptmvt(lowerx=c(-1,-1), upperx=c(0.5,0), mean=c(0,0), sigma=sigma, df=3, 
  lower=c(-1,-1), upper=c(1,1))