nPolyk: K-Statistics Master function

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

K-Statistics Master function

Description

The master function executes one of the functions to compute simple k-statistics (nKS), multivariate k-statistics (nKM), simple polykays (nPS) or multivariate polykays (nPM).

Usage

nPolyk( L = NULL, data = NULL, bhelp=NULL ) 

Arguments

L	vector of orders
data	vector of a (univariate or multivariate) sample data
bhelp	T=true or F=false

Details

The master function analizes the first two input variables and recalls one of the nKS, nKM, nPS or nPM functions in the kStatistics package.

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))

Value

float

the estimate of the (joint) cumulant or of the (joint) cumulant product

Note

The dimension of the vector with the sample data depends on the first parameter.

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

nKS, nKM, nPS, nPM

Examples

# 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:[1] -1.44706" which indicates the type of subfunction (nKS) called by 
# the master function nPolyk and gives the estimate of the third cumulant 
nPolyk(c(3),data1, TRUE) 
 
# Display "[1] -1.44706" (without the indication of the employed subfunction)
nPolyk(c(3),data1, FALSE)

# Display "PS:[1] 177.4233" which indicates the type of subfunction (nPS) called by 
# the master function nPolyk and gives the estimate of the product between the 
# variance k[2] and the mean k[1] 
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))

# Display "KM:[1] -23.7379" which indicates the type of subfunction (nKM) called by 
# the master function nPolyk and gives the estimate of k[2,1]  
nPolyk(c(2,1),data2,TRUE)

# Display "PM:[1] 48.43243" which indicates the type of subfunction (nPM) called by 
# the master function nPolyk and gives the estimate of k[2,1]*k[1,0]  
nPolyk( list(  c(2,1), c(1,0) ),data2,TRUE)

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