dbmss (version 1.2.4)

KinhomEnvelope: Estimation of the confidence envelope of the Kinhom function under its null hypothesis

Description

Simulates point patterns according to the null hypothesis and returns the envelope of Kinhom according to the confidence level.

Usage

KinhomEnvelope(NumberOfSimulations, Alpha, X, r, ReferenceType="", 
    SimulationType="RandomPosition", lambda=NULL)

Arguments

NumberOfSimulations

The number of simulations to run.

Alpha

The risk level.

X

A point pattern (ppp.object), marks must be a dataframe with two columns: PointType: labels, as factors. PointWeight: weights.

r

A vector of distances.

ReferenceType

One of the point types. Default is all point types.

SimulationType

A string describing the null hypothesis to simulate. The null hypothesis, may be "RandomPosition": points are drawn in an inhomogenous Poisson process (intensity is either lambda or estimated from X); "RandomLo

lambda

An estimation of the point pattern density, obtained by the density.ppp function.

Value

• A list:
• Simulations
  A matrix containing the simulated values (each line is a simulation, each column a value of Kinhom(R).
• Min
  A vector: the lower bound of the envelope.
• Max
  A vector: the upper bound of the envelope.

Details

This envelope is local, that is to say it is computed separately at each distance. See Loosmore and Ford (2006) for a discussion.

References

Kenkel, N. C. (1988). Pattern of Self-Thinning in Jack Pine: Testing the Random Mortality Hypothesis. Ecology 69(4): 1017-1024. Loosmore, N. B. and Ford, E. D. (2006). Statistical inference using the G or K point pattern spatial statistics. Ecology 87(8): 1925-1931.

See Also

Kinhom.r

Examples

data(paracou16)
# Keep only 20% of points to run this example
X <- rthin(paracou16, 0.2)
plot(X)

# Density of all trees
lambda <- density.ppp(X, bw.diggle(X))
plot(lambda)
V.americana <- X[X$marks$PointType=="V. Americana"]
plot(V.americana, add=TRUE)

# Calculate Kinhom according to the density of all trees
r <- 0:30
ActualValues.X <- Kinhom.r(X, r, "V. Americana", lambda)

# Calculate confidence envelope (should be 1000 simulations, reduced to 4 to save time)
NumberOfSimulations <- 4
Alpha <- .10
LocalEnvelope.X <- KinhomEnvelope(NumberOfSimulations, Alpha, X, r, , 
    SimulationType="RandomPosition", lambda=lambda)

# Plot
PlotResults(r, DivideByPiR2(ActualValues.X, r), lapply(LocalEnvelope.X, DivideByPiR2, r), 
    ylab="Kinhom / (pi R^2)", ReferenceValue=1)