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.

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
par(mar=c(1,1,1,1))
plot(wmppp(data.frame(X, Y, PointType)), which.marks=2, main="")
```

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.

```
data(paracou16)
# Plot (second column of marks is Point Types)
par(mar=c(1,1,1,1))
plot(paracou16, which.marks=2, leg.side="right", main="")
```

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:

```
plot(Mhat(paracou16, , "V. Americana", "Q. Rosea"), main="")
```

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

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

```
## Generating 100 simulations by evaluating expression ...
## 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
## 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
## 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100.
##
## Done.
```

Significant concentration is detected between about 10 and 20 meters.