| Type: | Package |
| Title: | Truncated Multivariate Normal and t Distribution Simulation |
| Version: | 0.1.3 |
| Date: | 2022-10-09 |
| Author: | Kaifeng Lu |
| Maintainer: | Kaifeng Lu <kaifenglu@gmail.com> |
| Description: | Simulation of random vectors from truncated multivariate normal and t distributions based on the algorithms proposed by Yifang Li and Sujit K. Ghosh (2015) <doi:10.1080/15598608.2014.996690>. |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| Imports: | Rcpp (≥ 1.0.7) |
| LinkingTo: | Rcpp, RcppArmadillo |
| RoxygenNote: | 7.2.1 |
| Suggests: | testthat (≥ 3.0.0), tmvmixnorm |
| Encoding: | UTF-8 |
| Config/testthat/edition: | 3 |
| NeedsCompilation: | yes |
| Packaged: | 2022-10-09 21:25:56 UTC; kaifeng |
| Repository: | CRAN |
| Date/Publication: | 2022-10-09 21:50:04 UTC |
Truncated Multivariate Normal and t Distribution Simulation
Description
Simulation of random vectors from truncated multivariate normal and t distributions based on the algorithms proposed by Yifang Li and Sujit K. Ghosh (2015) <doi:10.1080/15598608.2014.996690>. We allow the mean, lower and upper bounds to differ across samples to accommodate regression problems. The algorithms are implemented in C++ and hence are highly efficient.
Author(s)
Kaifeng Lu, kaifenglu@gmail.com
References
Yifang Li and Sujit K. Ghosh. Efficient Sampling Methods for Truncated Multivariate Normal and Student-t Distributions Subject to Linear Inequality Constraints. Journal of Statistical Theory and Practice. 2015;9:712-732. doi: 10.1080/15598608.2014.996690
Random Generation for Truncated Multivariate Normal
Description
Draws from truncated multivariate normal distribution subject to linear inequality constraints represented by a matrix.
Usage
rtmvnorm(
mean,
sigma,
blc = NULL,
lower,
upper,
init = NULL,
burn = 10,
n = NULL
)
Arguments
mean |
|
sigma |
|
blc |
|
lower |
|
upper |
|
init |
|
burn |
number of burn-in iterations. Defaults to 10. |
n |
number of random samples when |
Value
Returns an n x p matrix of random numbers following the
specified truncated multivariate normal distribution.
Examples
# Example 1: full rank blc
d = 3;
rho = 0.9;
sigma = matrix(0, d, d);
sigma = rho^abs(row(sigma) - col(sigma));
blc = diag(1,d);
n = 1000;
mean = matrix(rep(1:d,n), nrow=n, ncol=d, byrow=TRUE);
set.seed(1203)
result = rtmvnorm(mean, sigma, blc, -1, 1, burn=50)
apply(result, 2, summary)
# Example 2: use the alternative form of input
set.seed(1203)
result = rtmvnorm(mean=1:d, sigma, blc, -1, 1, burn=50, n=1000)
apply(result, 2, summary)
# Example 3: non-full rank blc
d = 3;
rho = 0.5;
sigma = matrix(0, d, d);
sigma = rho^abs(row(sigma) - col(sigma));
blc = matrix(c(1,1,1,0,1,0,1,0,1), ncol=d);
n = 100;
mean = matrix(rep(1:d,n), nrow=n, ncol=d, byrow=TRUE);
set.seed(1228)
result = rtmvnorm(mean, sigma, blc, -1, 1, burn=10)
apply(result, 2, summary)
# Example 4: non-full rank blc, alternative form of input
set.seed(1228)
result = rtmvnorm(mean=1:d, sigma, blc, -1, 1, burn=10, n=100)
apply(result, 2, summary)
# Example 5: means, lower, or upper bounds differ across samples
d = 3;
rho = 0.5;
sigma = matrix(0, d, d);
sigma = rho^abs(row(sigma) - col(sigma));
blc = matrix(c(1,0,1,1,1,0), ncol=d, byrow=TRUE)
n = 100;
set.seed(3084)
mean = matrix(runif(n*d), nrow=n, ncol=d);
result = rtmvnorm(mean, sigma, blc, -1, 1, burn=50)
apply(result, 2, summary)
Random Generation for Truncated Multivariate t
Description
Draws from truncated multivariate t distribution subject to linear inequality constraints represented by a matrix.
Usage
rtmvt(
mean,
sigma,
nu,
blc = NULL,
lower,
upper,
init = NULL,
burn = 10,
n = NULL
)
Arguments
mean |
|
sigma |
|
nu |
degrees of freedom for Student-t distribution. |
blc |
|
lower |
|
upper |
|
init |
|
burn |
number of burn-in iterations. Defaults to 10. |
n |
number of random samples when |
Value
Returns an n x p matrix of random numbers following the
specified truncated multivariate t distribution.
Examples
# Example 1: full rank blc
d = 3;
rho = 0.5;
sigma = matrix(0, d, d);
sigma = rho^abs(row(sigma) - col(sigma));
nu = 10;
blc = diag(1,d);
n = 1000;
mean = matrix(rep(1:d,n), nrow=n, ncol=d, byrow=TRUE);
set.seed(1203)
result = rtmvt(mean, sigma, nu, blc, -1, 1, burn=50)
apply(result, 2, summary)
# Example 2: use the alternative form of input
set.seed(1203)
result = rtmvt(mean=1:d, sigma, nu, blc, -1, 1, burn=50, n)
apply(result, 2, summary)
# Example 3: non-full rank blc, different means
d = 3;
rho = 0.5;
sigma = matrix(0, d, d);
sigma = rho^abs(row(sigma) - col(sigma));
nu = 10;
blc = matrix(c(1,0,1,1,1,0), nrow=d-1, ncol=d, byrow=TRUE)
n = 100;
set.seed(3084)
mean = matrix(runif(n*d), nrow=n, ncol=d);
result = rtmvt(mean, sigma, nu, blc, -1, 1, burn=50)
apply(result, 2, summary)
Random Generation for Truncated Univariate Normal
Description
Draws from truncated univariate normal distribution within an interval.
Usage
rtnorm(mean, sd = 1, lower, upper, n = NULL)
Arguments
mean |
vector of means. The length is the number of observations. |
sd |
standard deviation. Defaults to 1. |
lower |
a scalar of lower bound for truncation, or a vector of
lower bounds with the same length as |
upper |
a scalar of upper bound for truncation, or a vector of
upper bounds with the same length as |
n |
number of random samples when |
Value
Returns a vector of random numbers following the specified truncated univariate normal distribution.
Examples
set.seed(1203)
x = rtnorm(mean=rep(1,1000), sd=2, lower=-2, upper=3)
summary(x)
# use the alternative form of input
set.seed(1203)
x = rtnorm(mean=1, sd=2, lower=-2, upper=3, n=1000)
summary(x)