phi_p {LHD}

Calculate the phi_p Criterion

Description

phi_p returns the phi_p criterion of an LHD

Usage

phi_p(X, p = 15, q = 1)

Arguments

X

A matrix object. In general, X stands for the design matrix.

p

A positive integer, which is the parameter in the phi_p formula, and p is prefered to be large. The default is set to be 15.

q

The default is set to be 1, and it could be either 1 or 2. If q is 1, dij is the Manhattan (rectangular) distance. If q is 2, dij is the Euclidean distance.

Value

If all inputs are logical, then the output will be a positive number indicating phi_p. \phi_p = (\sum_{i=1}^{n-1}\sum_{j=i+1}^{n}dij^{-p})^{1/p}, where dij = \left\{ \sum_{k=1}^{m} \vert x_{ik}-x_{jk}\vert ^q \right\}^{1/q}

References

Jin, R., Chen, W., and Sudjianto, A. (2005) An efficient algorithm for constructing optimal design of computer experiments. Journal of Statistical Planning and Inference, 134, 268-287.

Examples

#create a toy LHD with 5 rows and 3 columns
toy=rLHD(n=5,k=3);toy

#Calculate the phi_p criterion of toy with default setting
phi_p(X=toy)

#Calculate the phi_p criterion of toy with p=50 and q=2
phi_p(X=toy,p=50,q=2)