kStatistics (version 2.0)

powS: Power sums

Description

Given one or more lists of numbers, computes the value of the power sum symmetric polynomial with fixed degrees in one or more sets of variables replaced by a given list of numbers.

Usage

powS(vn,lvd)

Arguments

vn

vector of powers (degrees)

lvd

list of numbers

Value

integer

value of the power sum symmetric polynomial

Details

Given the lists (x[1],x[2],...), (y[1],y[2],...), (z[1],z[2],...), ... in L and the integers (n,m,j,...) in vn, the function powS( vn ,L ) returns (x[1]^n)*(y[1]^m)*(z[1]^j)*...+(x[2]^n)*(y[2]^m)*(z[2]^j)*+...See also the examples.

References

E. Di Nardo, G. Guarino, D. Senato (2008) Symbolic computation of moments of sampling distributions. Comp. Stat. Data Analysis. 52(11), 4909-4922. (download from http://arxiv.org/abs/0806.0129)

Examples

# NOT RUN {
# Return 1^3 + 2^3 + 3^3 = 36
powS(c(3), list(c(1),c(2),c(3))) 

# Return (1^3 * 4^2) + (2^3 * 5^2) + (3^3 * 6^2) = 1188
powS(c(3,2),list(c(1,4),c(2,5),c(3,6))) 

# }