| powS {kStatistics} | 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)))