kStatistics (version 2.0)

nPS: Simple Polykays

Description

Given a sample data, compute an estimate of a product of population cumulants using simple Polykays (generalized k-statistics).

Usage

nPS( v, V )

Arguments

v

vector of integers

V

vector of sample data

Value

float

estimate of the polykay of order v

Details

Products of kstatistics are known as polykays. They are unbiased estimators of products of cumulants of a distribution and are expressed in terms of the power sum symmetric polynomials in the random variables of the sample. Thus, for the given sample data, nPS(c(i,j,...),data) computes an estimate of the product k[i]*k[j]*... where k[i], k[j], ... are cumulants of the population distribution.

References

E. Di Nardo, G. Guarino, D. Senato (2008) An unifying framework for k-statistics, polykays and their generalizations. Bernoulli. 14(2), 440-468. (download from http://arxiv.org/pdf/math/0607623.pdf)

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)

E. Di Nardo, G. Guarino, D. Senato (2009) A new method for fast computing unbiased estimators of cumulants. Statistics and Computing, 19, 155-165. (download from https://arxiv.org/abs/0807.5008)

P. McCullagh, J. Kolassa (2009), Scholarpedia, 4(3):4699. http://www.scholarpedia.org/article/Cumulants

See Also

nPolyk, nKS, nKM, nPM

Examples

# NOT RUN {
# Data assignment
data<-c(16.34, 10.76, 11.84, 13.55, 15.85, 18.20, 7.51, 10.22, 12.52, 14.68, 16.08, 
19.43,8.12, 11.20, 12.95, 14.77, 16.83, 19.80, 8.55, 11.58, 12.10, 15.02, 16.83, 
16.98, 19.92, 9.47, 11.68, 13.41, 15.35, 19.11)

# Return the estimate of the product k[2]*k[1], where k[1] and k[2] are respectively 
# the mean and the variance of the population distribution  
nPS(c(2,1), data) 

# }