# phi_p

From LHD v0.1.0
0th

Percentile

##### Calculate the phi_p Criterion

phi_p returns the phi_p criterion of a LHD

##### Usage
phi_p(X, p, q = 1)
##### Arguments
X

A Matrix.

p

A positive integer.

q

The default is set to be 1, and it could be either 1 or 2.

##### Details

• X stands for the design matrix.

• p is the parameter in the phi_p formula (see Note Section below), and p is prefered to be large.

• If q is 1 (the default setting), dij is the 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.

##### Note

\phi_p = (\sum_{i=1}^{n-1}\sum_{j=i+1}^{n}dij^{-p})^{1/p}

##### 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.

• phi_p
##### Examples
# NOT RUN {
#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 q and p=50)
phi_p(X=toy,p=50)

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

Documentation reproduced from package LHD, version 0.1.0, License: MIT + file LICENSE

### Community examples

Looks like there are no examples yet.