kStatistics (version 1.0)

nPolyk: K-Statistics Master function

Description

The master function executes one of 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

array of orders

data

array 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. Vol. 14(2), 440-468. (download from http://www.elviradinardo.it/lavori1.html)

E. Di Nardo, G. Guarino, D. Senato (2008) Symbolic computation of moments of sampling distributions. Comp. Stat. Data Analysis Vol. 52(11), 4909-4922, (download from http://www.elviradinardo.it/lavori1.html)

E. Di Nardo, G. Guarino, D. Senato (2009) A new method for fast computing unbiased estimators of cumulants. Statistics and Computing, Vol. 19, 155-165. (download from http://www.elviradinardo.it/lavori1.html)

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

See Also

nKS, nKM, nPS, nPM

Examples

# NOT RUN {
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)

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

nPolyk( list(  c(2), c(1) ),data1,TRUE)
# generate the estimate of c_2*c_1 with the indication of the employed subfunction
# PS:[1] 177.4233

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))

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

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