kStatistics (version 2.0)

nPolyk: K-Statistics Master function

Description

The master function executes one of the functions to generate simple kstatistics (nKS), multivariate kstatistics (nKM), simple polykays (nPS), multivariate polykays (nPM) of given orders.

Usage

nPolyk( L, data, bhelp=NULL )

Arguments

L

vector of orders

data

vector of (multivariate) sample data

bhelp

T=true or F=false

Value

float

estimate of (joint) cumulant (product)

Details

The master function analizes the first and the second parameters and recall one of the functions nKS, nKM, nPS, nPM in the package kStatistics. Given a sample data: 1) simple k-statistics are computed using nPolyk(c(r), data)) or nPolyk(list(c(r)), data)) 2) multivariate k-statistics are computed using nPolyk(c(r, s), data)) or nPolyk( list(c(r, s)), data)) 3) simple polykays are computed using nPolyk(list(c(r),c(s)...),data)) 4) multivariate polykays are computed using nPolyk(list(c(r1, r2,...),c(s1, s2,...),...),data))

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

nKS, nKM, nPS, nPM

Examples

# NOT RUN {
# Data assignment
data1<-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)

# display "KS" which indicates the type of subfunction (nKS) called by the master function nPolyk
# KS:[1] -1.44706
nPolyk(c(3),data1, TRUE) 
 
# Produce 
# [1] -1.44706 (without indication of the employed subfunction)
nPolyk(c(3),data1, FALSE)

# Return the estimate of k[2]*k[1] with the indication of the employed subfunction
# PS:[1] 177.4233
nPolyk( list(  c(2), c(1) ),data1,TRUE)

# Data assignment
data2<-list(c(5.31,11.16),c(3.26,3.26),c(2.35,2.35),c(8.32,14.34),c(13.48,49.45),
c(6.25,15.05),c(7.01,7.01),c(8.52,8.52),c(0.45,0.45),c(12.08,12.08),c(19.39,10.42))

# Return the estimate of k[2,1] with the indication of the employed subfunction
# KM:[1] -23.7379
nPolyk(c(2,1),data2,TRUE)

# Return the estimate of k[2,1]*k[1,0] with the indication of the employed subfunction
# PM:[1] 48.43243
nPolyk( list(  c(2,1), c(1,0) ),data2,TRUE)

# }