# miplot

0th

Percentile

##### Morishita Index Plot

Displays the Morishita Index Plot of a spatial point pattern.

Keywords
spatial, nonparametric
miplot(X, ...)
##### Arguments
X
A point pattern (object of class "ppp") or something acceptable to as.ppp.
...
Optional arguments to control the appearance of the plot.
##### Details

Morishita (1959) defined an index of spatial aggregation for a spatial point pattern based on quadrat counts. The spatial domain of the point pattern is first divided into $Q$ subsets (quadrats) of equal size and shape. The numbers of points falling in each quadrat are counted. Then the Morishita Index is computed as $$\mbox{MI} = Q \frac{\sum_{i=1}^Q n_i (n_i - 1)}{N(N-1)}$$ where $n_i$ is the number of points falling in the $i$-th quadrat, and $N$ is the total number of points. If the pattern is completely random, MI should be approximately equal to 1. Values of MI greater than 1 suggest clustering.

The Morishita Index plot is a plot of the Morishita Index MI against the linear dimension of the quadrats. The point pattern dataset is divided into $2 \times 2$ quadrats, then $3 \times 3$ quadrats, etc, and the Morishita Index is computed each time. This plot is an attempt to discern different scales of dependence in the point pattern data.

• None.

##### References

M. Morishita (1959) Measuring of the dispersion of individuals and analysis of the distributional patterns. Memoir of the Faculty of Science, Series E2, Kyushu University. Pages 215--235.

• miplot
##### Examples
data(longleaf)
miplot(longleaf)
opa <- par(mfrow=c(2,3))
data(cells)
data(japanesepines)
data(redwood)
plot(cells)
plot(japanesepines)
plot(redwood)
miplot(cells)
miplot(japanesepines)
miplot(redwood)
par(opa)
Documentation reproduced from package spatstat, version 1.23-2, License: GPL (>= 2)

### Community examples

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