Kinhomhat {dbmss} | R Documentation |

## Estimation of the inhomogenous K function

### Description

Estimates the *Kinhom* function

### Usage

```
Kinhomhat(X, r = NULL, ReferenceType = "", lambda = NULL, CheckArguments = TRUE)
```

### Arguments

`X` |
A weighted, marked, planar point pattern ( |

`r` |
A vector of distances. If |

`ReferenceType` |
One of the point types. Default is all point types. |

`lambda` |
An estimation of the point pattern density, obtained by the |

`CheckArguments` |
Logical; if |

### Details

*Kinhom* is a cumulative, topographic measure of an inhomogenous point pattern structure.

By default, density estimation is performed at points by `density.ppp`

using the optimal bandwith (`bw.diggle`

). It can be calculated separately (see example), including at pixels if the point pattern is too large for the default estimation to succeed, and provided as the argument `lambda`

:
Arbia et al. (2012) for example use another point pattern as a reference to estimate density.

Bivariate *Kinhom* is not currently supported.

### Value

An object of class `fv`

, see `fv.object`

, which can be plotted directly using `plot.fv`

.

### Note

The computation of `Kinhomhat`

relies on spatstat functions `Kinhom`

, `density.ppp`

and `bw.diggle`

.

### References

Baddeley, A. J., J. Moller, et al. (2000). Non- and semi-parametric estimation of interaction in inhomogeneous point patterns. *Statistica Neerlandica* 54(3): 329-350.

Arbia, G., G. Espa, et al. (2012). Clusters of firms in an inhomogeneous space: The high-tech industries in Milan. *Economic Modelling* 29(1): 3-11.

### See Also

### Examples

```
data(paracou16)
# Density of all trees
lambda <- density.ppp(paracou16, bw.diggle(paracou16))
plot(lambda)
# Reduce the point pattern to one type of trees
V.americana <- paracou16[paracou16$marks$PointType=="V. Americana"]
plot(V.americana, add=TRUE)
# Calculate Kinhom according to the density of all trees
r <- 0:30
autoplot(Kinhomhat(paracou16, r, "V. Americana", lambda), ./(pi*r^2) ~ r)
```

*dbmss*version 2.9-0 Index]