nPS: Simple Polykays

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

Simple Polykays

Description

Given a data sample, the function returns an estimate of a product of cumulants with fixed orders.

Usage

nPS( v = NULL, V = NULL) 

Arguments

v	vector of integers
V	vector of a data sample

Details

Simple polykays or generalized k-statistics are unbiased estimators of cumulant products with minimum variance. See the referred papers to read more about these estimators. Simple polykays are usually expressed in terms of power sum symmetric polynomials in the i.i.d. random variables of the sample. Thus, for the input sample data, running nPS(c(i,j,...),data) returns an estimate of the product k[i]*k[j]*... with k[i], k[j], ... the cumulants of the population distribution and v=(i,j,...) their fixed orders.

Value

float

the estimate of the polykay

Note

Called by the master nPolyk function in the kStatistics package.

Author(s)

Elvira Di Nardo [e-mail],
Giuseppe Guarino [e-mail]

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 https://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 https://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

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

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