roi {nsRFA} | R Documentation

## Region of influence

### Description

Formation of clusters for Regional Frequency Analysis: region of influence (Burn, 1990).

### Usage

     roi (p.ungauged, p.gauged, cod.p, x=NULL, cod=NULL)
     roi.hom (p.ungauged, p.gauged, cod.p, x, cod,
       test="HW", limit=2, Nsim=500, index=2)
     roi.st.year (p.ungauged, p.gauged, cod.p, x, cod,
       test="HW", station.year=500, Nsim=500, index=2)

### Arguments

`x` | vector representing data from many samples defined with `cod`
`cod` | array that defines the data subdivision among sites
`index` | if `index`=1 samples are divided by their average value; if `index`=2 (default) samples are divided by their median value
`p.ungauged` | parameters of the ungauged site (1 row)
`p.gauged` | parameters of gauged sites
`cod.p` | code of gauged sites
`test` | homogeneity test to apply: `"HW"` (default) or `"AD"` (in `roi.st.year` you can choose `"HW and AD"` too
`limit` | limit over which regions must be considered heterogeneous: for example 2 for `"HW"` or .95 for `"AD"`
`Nsim` | number of simulations in `"HW"` or `"AD"` tests
`station.year` | number of station years to form the region

### Details

The Euclidean distance is used. Given p different classification variables, the distance between two elements i and j is:

d_ij = sqrt{1/p sum[h from 1 to p](x_hi - x_hj)^2}

where x_hi is the value of the h-th variable of the i-th element.

### Value

`roi` returns the ‘region of influence’ for the site defined with `p.ungauged`. It the gauged sites ordered according to the euclidean distance against the site of interest (the distance is evaluated in the space defined by parameters `p.ungauged` and `p.gauged`). If `x=NULL` and `cod=NULL` (default), a data.frame with the ordered sites and the distances against the site of interest is returned. If `x` and `cod` are provided, the data.frame will contain also statistics of samples (number of data `n` and L-moments).
`roi.hom` returns the ‘region of influence’ for the site defined with `p.ungauged`. It returns codes of gauged sites that form an homogeneous region according to the Hosking and Wallis `"HW"` or Anderson-Darling `"AD"` tests. The region is formed using distances in the space defined by parameters `p.ungauged` and `p.gauged`.
`roi.st.year` returns the ‘region of influence’ for the site defined with `p.ungauged`. It returns codes of gauged sites that form a region and the risult of homogeneity tests, according to the station-year criterion. It also return the similarity ranking factor S_i, the weights w_i and the regional L-moments as evaluated in the Flood Estimation Handbook (Robson and Reed, 1999). The region is formed using distances in the space defined by parameters `p.ungauged` and `p.gauged`.

### Note

For information on the package and the Author, and for all the references, see `nsRFA`.

### See Also

`traceWminim`, `AD.dist`, `HOMTESTS` for the definition of the Hosking and Wallis `"HW"` or Anderson-Darling `"AD"` tests.

### Examples

    data(hydroSIMN)
    parameters
    summary(parameters)

    annualflows
    summary(annualflows)
    x <- annualflows["dato"][,]
    cod <- annualflows["cod"][,]

    roi(parameters[5,3:5],parameters[-5,3:5],parameters[-5,1])
    roi(parameters[5,3:5],parameters[-5,3:5],parameters[-5,1],x,cod)

    # roi.hom
    #roi.hom(parameters[5,3:5],parameters[-5,3:5],parameters[-5,1],x,cod)
                                # it takes some time
    #roi.hom(parameters[5,3:5],parameters[-5,3:5],parameters[-5,1],x,cod,
    #        test="AD",limit=.95)      # it takes some time

    #roi.hom(parameters[8,3:5],parameters[-8,3:5],
    #         parameters[-8,1],x,cod)    # it takes some time

    # roi.st.year
    roi.st.year(parameters[5,3:5],parameters[-5,3:5],
                parameters[-5,1],x,cod)
    roi.st.year(parameters[5,3:5],parameters[-5,3:5],parameters[-5,1],
                x,cod,test="AD",station.year=100)

[Package nsRFA version 0.6-9 Index]