Description
Symbolic Central and Noncentral Moments of the Multivariate Normal Distribution.
Description
Symbolic central and non-central moments of the multivariate normal distribution. Computes a standard representation, LateX code, and values at specified mean and covariance matrices.
README.md
symmoments
Symbolically computes and numerically evaluates multivariate normal moments , where , in terms of mu and S elements.
Installation
You can install the development version of symmoments from GitHub with:
# install.packages("pak")
pak::pak("FloSchuberth/symmoments")
Example
This is a basic example which shows you how to solve a common problem:
library(symmoments)
# Compute the moment for the 4-dimensional moment c(1,2,3,4):
callmultmoments(c(1,2,3,4))
#> E[ X1^1 X2^2 X3^3 X4^4 ]:
#> coef S(1,1) S(1,2) S(1,3) S(1,4) S(2,2) S(2,3) S(2,4) S(3,3) S(3,4) S(4,4)
#> 1 72 0 0 0 1 0 0 2 1 1 0
#> 2 144 0 0 0 1 0 1 1 0 2 0
#> 3 72 0 0 0 1 0 1 1 1 0 1
#> 4 72 0 0 0 1 0 2 0 0 1 1
#> 5 24 0 0 0 1 1 0 0 0 3 0
#> 6 36 0 0 0 1 1 0 0 1 1 1
#> 7 72 0 0 1 0 0 0 2 0 2 0
#> 8 36 0 0 1 0 0 0 2 1 0 1
#> 9 144 0 0 1 0 0 1 1 0 1 1
#> 10 18 0 0 1 0 0 2 0 0 0 2
#> 11 36 0 0 1 0 1 0 0 0 2 1
#> 12 9 0 0 1 0 1 0 0 1 0 2
#> 13 48 0 1 0 0 0 0 1 0 3 0
#> 14 72 0 1 0 0 0 0 1 1 1 1
#> 15 72 0 1 0 0 0 1 0 0 2 1
#> 16 18 0 1 0 0 0 1 0 1 0 2
# Print the representation of the 4-dimensional moment c(1,2,3,4):
print(callmultmoments(c(1,2,3,4)))
#> E[ X1^1 X2^2 X3^3 X4^4 ]:
#> coef S(1,1) S(1,2) S(1,3) S(1,4) S(2,2) S(2,3) S(2,4) S(3,3) S(3,4) S(4,4)
#> 1 72 0 0 0 1 0 0 2 1 1 0
#> 2 144 0 0 0 1 0 1 1 0 2 0
#> 3 72 0 0 0 1 0 1 1 1 0 1
#> 4 72 0 0 0 1 0 2 0 0 1 1
#> 5 24 0 0 0 1 1 0 0 0 3 0
#> 6 36 0 0 0 1 1 0 0 1 1 1
#> 7 72 0 0 1 0 0 0 2 0 2 0
#> 8 36 0 0 1 0 0 0 2 1 0 1
#> 9 144 0 0 1 0 0 1 1 0 1 1
#> 10 18 0 0 1 0 0 2 0 0 0 2
#> 11 36 0 0 1 0 1 0 0 0 2 1
#> 12 9 0 0 1 0 1 0 0 1 0 2
#> 13 48 0 1 0 0 0 0 1 0 3 0
#> 14 72 0 1 0 0 0 0 1 1 1 1
#> 15 72 0 1 0 0 0 1 0 0 2 1
#> 16 18 0 1 0 0 0 1 0 1 0 2
# Compute the LaTeX representation of the central moment c(1,2,3,4):
toLatex(callmultmoments(c(1,2,3,4)))
#> [1] "E[X_{1}^{1}X_{2}^{2}X_{3}^{3}X_{4}^{4}]=\\\\"
#> [2] "18\\sigma_{1,2}\\sigma_{2,3}\\sigma_{3,3}\\sigma_{4,4}^{2}+"
#> [3] "72\\sigma_{1,2}\\sigma_{2,3}\\sigma_{3,4}^{2}\\sigma_{4,4}+"
#> [4] "72\\sigma_{1,2}\\sigma_{2,4}\\sigma_{3,3}\\sigma_{3,4}\\sigma_{4,4}+"
#> [5] "48\\sigma_{1,2}\\sigma_{2,4}\\sigma_{3,4}^{3}+\\\\"
#> [6] "9\\sigma_{1,3}\\sigma_{2,2}\\sigma_{3,3}\\sigma_{4,4}^{2}+"
#> [7] "36\\sigma_{1,3}\\sigma_{2,2}\\sigma_{3,4}^{2}\\sigma_{4,4}+"
#> [8] "18\\sigma_{1,3}\\sigma_{2,3}^{2}\\sigma_{4,4}^{2}+"
#> [9] "144\\sigma_{1,3}\\sigma_{2,3}\\sigma_{2,4}\\sigma_{3,4}\\sigma_{4,4}+\\\\"
#> [10] "36\\sigma_{1,3}\\sigma_{2,4}^{2}\\sigma_{3,3}\\sigma_{4,4}+"
#> [11] "72\\sigma_{1,3}\\sigma_{2,4}^{2}\\sigma_{3,4}^{2}+"
#> [12] "36\\sigma_{1,4}\\sigma_{2,2}\\sigma_{3,3}\\sigma_{3,4}\\sigma_{4,4}+"
#> [13] "24\\sigma_{1,4}\\sigma_{2,2}\\sigma_{3,4}^{3}+\\\\"
#> [14] "72\\sigma_{1,4}\\sigma_{2,3}^{2}\\sigma_{3,4}\\sigma_{4,4}+"
#> [15] "72\\sigma_{1,4}\\sigma_{2,3}\\sigma_{2,4}\\sigma_{3,3}\\sigma_{4,4}+"
#> [16] "144\\sigma_{1,4}\\sigma_{2,3}\\sigma_{2,4}\\sigma_{3,4}^{2}+"
#> [17] "72\\sigma_{1,4}\\sigma_{2,4}^{2}\\sigma_{3,3}\\sigma_{3,4}\\\\"
# evaluate the moment c(1,2,3,4) at the following variance-covariance matrix
# 4 2 1 1
# 2 3 1 1
# 1 1 2 1
evaluate(callmultmoments(c(1,2,3,4)), c(4,2,1,1,3,1,1,2,1,2))
#> [1] 3480