symmoments-package: Symbolically compute and numerically evaluate multivariate...

In symmoments: Symbolic Central and Noncentral Moments of the Multivariate Normal Distribution

Description

Symbolically computes and numerically evaluates multivariate normal moments E[X1**2 *...* Xn**n], where (X1,...,Xn) ~ N(mu,S), in terms of mu and S elements.

Produces Latex code for the moment.

Computes numerical moments at specified means and covariance matrices.

Also converts between moment L-matrices, phylo objects, and matching objects.

Details

Package:	symmoments
Type:	Package
Version:	1.2
Date:	2018-05-30
License:	GPL 2
LazyLoad:	yes

A representation of a central moment of the multivariate normal distribution, given by a positive integer vector c(k1,k2,...,kn), is obtained from the function callmultmoments. This function initializes variables and calls the function multmoments which determines a representation of a multivariate moment using a recursive algorithm. The representation is given class 'moment'.

The print method prints the representation of a multivariate moment.

The toLatex method uses the output of callmultmoments to determine the LaTeX code for the moment sorted lexicographically.

The generic evaluate method uses the output of callmultmoments to determine the value of the moment for a specified covariance matrix.

The simulate method is used to approximate a (possibly non-central) moment using Monte Carlo integration.

The following functions compute non-central moments and do related computations:

The toLatex_noncentral function computes the Latex representations of a non-central moment.

The evaluate_noncentral computes the value of a non-central moment.

The evaluate_expected.polynomial function evaluates the expected value of a multivariate polynomial defined by a list, multipol object, or mpoly object.

The convert.multipol function converts between multipol objects and multivariate polynomials defined by lists.

The convert.mpoly function converts between mpoly objects and multivariate polynomials defined by lists.

The tounsorted function converts a sorted moment (e.g. m123) to an unsorted moment (e.g. m312).

The make.all.moments function computes all moments up to a specified size and places them in the symmoments environment.

The integrate.polynomial function integrates a multivariate polynomial against the normal distribution using ordinary integration.

The functions toMoment, toNewick, and toMatching convert among moment L-matrices, Newick trees, and ape matching objects.

Note

The mvtnorm package must be loaded for the simulate method. The cubature package must be loaded for the integrate.polynomial function. The combinat package must be loaded for the toMoment function.

Author(s)

Maintainer: Kem Phillips <[e-mail]>

References

K Phillips, Symbolic Computation of the Central Moments of the Multivariate Normal Distribution, Journal of Statistical Software, 2010.

Examples

# Compute the moment for the 4-dimensional moment c(1,2,3,4):
callmultmoments(c(1,2,3,4)) 

# Print the representation of the 4-dimensional moment c(1,2,3,4):
print(callmultmoments(c(1,2,3,4))) 

# Compute the LaTeX representation of the central moment c(1,2,3,4):
toLatex(callmultmoments(c(1,2,3,4)))

# Write the LaTeX representation to a file using the standard R function (not run):
# writeLines(callmultmoments(c(1,2,3,4))),con="yourfilename", sep = "\n")

# 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))

# Using 10000 samples, estimate the central moment for c(2,4) at the covariance matrix (not run)
#  2 1
#  1 4

# and mean (0,0)
library(mvtnorm)
simulate(callmultmoments(c(2,4)),10000,NULL,c(0,0),c(2,1,1,4))

# Compute Latex representation of a non-central moment
# as.matrix(toLatex_noncentral(c(1,3))) 

# Create all 2-dimensional moment objects with exponents up to 3 
# First create the symmoments environment if it does not exist
# symmoments <- new.env()
# make.all.moments(c(3,3))

# Evaluate a non-central moment at a specified mean and covariance matrix
# Note that this invocation requires moments of order up to c(1,3)
# to exist in environment symmoments.
# evaluate_noncentral(c(1,3),c(1,2),c(1,0,1))

# Create an mpoly object 
library(mpoly)
t0 <- mpoly(list(c(coef=3,x1=2),c(coef=2,x1=1,x2=3),
                   c(coef=-4,z=2),c(coef=1,x1=1,x2=2,z=1)))  
                     
# Convert an mpolyobject to a moment object
t1 <<- convert.mpoly(t0)      

# Convert a moment object to a multipol object
t2 <<- convert.multipol(t1)

# Convert from multipol back to mpoly through moment

mpoly(convert.mpoly(convert.multipol(t2)))     

# Evaluate the expected value of a multivariate polynomial
# Required moments must exist in environment symmoments.

# evaluate_expected.polynomial(t0,c(1,2,3),c(1,0,0,1,0,1))

# Create a Newick representation of a tree
exam.Newick      <- "(((a,b),c),d);"

# Convert to phylo format
library(ape)
exam.phylo       <- read.tree(text=exam.Newick)

# Convert to matching format
exam.matching    <- as.matching(exam.phylo)

# Convert to L-matrix format
exam.L.matrix    <- toMoment(exam.matching)

symmoments documentation built on March 26, 2020, 6:28 p.m.