dbmss (version 1.2.4)

KmmEnvelope: Estimation of the confidence envelope of the Lmm function under its null hypothesis

Description

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

Usage

KmmEnvelope(NumberOfSimulations, Alpha, X, r, ReferenceType = "")

Arguments

NumberOfSimulations

The number of simulations to draw.

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. Others are ignored. Default is all point types.

Value

• A list:
• Simulations
  A matrix containing the simulated values (each line is a simulation, each column a value of Kmm(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

Kmm.r

Examples

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

# Calculate Kmm
r <- seq(0, 30, 2)
ActualValues.X <- Kmm.r(X, r)

# Calculate confidence envelope (should be 1000 simulations, reduced to 10 to save time)
NumberOfSimulations <- 10
Alpha <- .10
LocalEnvelope.X <- KmmEnvelope(NumberOfSimulations, Alpha, X, r)

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