varshannonZ {SpatEntropy}

Estimated variance of Shannon's entropy of Z.

Description

This function estimates the variance of Shannon's entropy of Z, where Z identifies pairs of categories of the original study variable.

Usage

varshannonZ(data)

Arguments

data

A data matrix or vector, can be numeric, factor, character, ... Alternatively, a marked ppp object.

Details

varshannonZ estimates the variance of the maximum likelihood estimator of Shannon's entropy of Z given by shannonZ. The variance is

V(H(Z))=H(Z)_2- H(Z)^2

, where

H(Z)_2=\sum p(z_r)\log(1/p(z_r))^2

. The function is able to work with lattice data with missing data, as long as they are specified as NAs: missing data are ignored in the computations.

Value

the estimated variance of Shannon's entropy of Z.

Examples

#NON SPATIAL DATA
data=sample(1:5, 50, replace=TRUE)
varshannonZ(data)

#POINT DATA
data.pp=runifpoint(100, win=square(10))
marks(data.pp)=sample(c("a","b","c"), 100, replace=TRUE)
varshannonZ(marks(data.pp))

#LATTICE DATA
data.lat=matrix(sample(c("a","b","c"), 100, replace=TRUE), nrow=10)
varshannonZ(data.lat)