powS: Power sums
In kStatistics: Unbiased Estimators for Cumulant Products and Faa Di Bruno's Formula

powS	R Documentation

Power sums

Description

The function returns the value of the power sum symmetric polynomial, with fixed degrees and in one or more sets of variables, when the variables are substituted with the input lists of numerical values.

Usage

powS(vn = NULL, lvd = NULL)

Arguments

`vn`	vector of integers (the powers of the indeterminates)
`lvd`	list of numerical values in place of the variables

Details

Given the lists of numerical values (x[1],x[2],...), (y[1],y[2],...), (z[1],z[2],...), ... in the input parameter lvd and the integers (n,m,j,...) in the input parameter vn, the powS function returns the value of (x[1]^n)*(y[1]^m)*(z[1]^j)*...+(x[2]^n)*(y[2]^m)*(z[2]^j)*+....

Value

integer

the value of the polynomial

Note

Called by the nKS, nKM, nPS and nPM functions in the kStatistics package.

Author(s)

Elvira Di Nardo elvira.dinardo@unito.it,
Giuseppe Guarino giuseppe.guarino@rete.basilicata.it

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 https://arxiv.org/abs/0806.0129)

Examples


# 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)))

kStatistics documentation built on June 8, 2022, 5:05 p.m.