The *dbmss* package allows simple computation of spatial
statistic functions of distance to characterize the spatial structures
of mapped objects, including classical ones (Ripley’s K and others) and
more recent ones used by spatial economists (Duranton and Overman’s
\(K_d\), Marcon and Puech’s \(M\)). It relies on *spatstat* for
some core calculation.

This vignette contains a quick introduction.

## Data

The main data format is `wmppp`

for weighted, marked point
pattern. It inherits from the `ppp`

class of the
*spatstat* package.

A `wmppp`

object can be created from the coordinates of
points, their type and their weight.

```
library("dbmss")
# Draw the coordinates of 10 points
X <- runif(10)
Y <- runif(10)
# Draw the point types.
PointType <- sample(c("A", "B"), 10, replace=TRUE)
# Plot the point pattern. Weights are set to 1 ant the window is adjusted
autoplot(wmppp(data.frame(X, Y, PointType)))
```

An example dataset is provided: it is a point pattern from the Paracou forest in French Guiana. Two species of trees are identified, other trees are of type “Other”. Point weights are their basal area, in square centimeters.

```
# Plot (second column of marks is Point Types)
autoplot(paracou16,
labelSize = expression("Basal area (" ~cm^2~ ")"),
labelColor = "Species")
```

## Main functions

The main functions of the packages are designed to calculate distance-based measures of spatial structure. Those are non-parametric statistics able to summarize and test the spatial distribution (concentration, dispersion) of points.

The classical, topographic functions such as Ripley’s *K* are
provided by the *spatstat* package and supported by
*dbmss* for convenience.

Relative functions are available in *dbmss* only. These are
the \(M\) and \(m\) and \(K_d\) functions.

The bivariate \(M\) function can be
calculated for *Q. Rosea* trees around *V. Americana*
trees:

## Confidence envelopes

Confidence envelopes of various null hypotheses can be calculated.
The univariate distribution of *Q. Rosea* is tested against the
null hypothesis of random location.

`autoplot(KdEnvelope(paracou16, , ReferenceType="Q. Rosea", Global=TRUE), main="")`

Significant concentration is detected between about 10 and 20 meters.