Ktest {dbmss} | R Documentation |

## Test of a point pattern against Complete Spatial Randomness

### Description

Tests the point pattern against CSR using values of the *K* function

### Usage

```
Ktest(X, r)
```

### Arguments

`X` |
A point pattern ( |

`r` |
A vector of distances. |

### Details

The test returns the risk to reject CSR erroneously, i.e. the p-value of the test, based on the distribution of the *K* function.

If `r`

includes 0, it will be silently removed because no neighbor point can be found at distance 0.
The longer `r`

, the more accurate the test is in theory but at the cost of computation time first, and of computation accuracy then because a matrix of size the length of `r`

must be inverted.
10 values in `r`

seems to be a reasonable choice.

### Value

A p-value.

### Author(s)

Gabriel Lang <Gabriel.Lang@agroparistech.fr>, Eric Marcon<Eric.Marcon@agroparistech.fr>

### References

Lang, G. and Marcon, E. (2013). Testing randomness of spatial point patterns with the Ripley statistic. *ESAIM: Probability and Statistics.* 17: 767-788.

Marcon, E., S. Traissac, and Lang, G. (2013). A Statistical Test for Ripley's Function Rejection of Poisson Null Hypothesis. *ISRN Ecology* 2013(Article ID 753475): 9.

### See Also

### Examples

```
# Simulate a Matern (Neyman Scott) point pattern
nclust <- function(x0, y0, radius, n) {
return(runifdisc(n, radius, centre=c(x0, y0)))
}
X <- rNeymanScott(20, 0.1, nclust, radius=0.2, n=5)
autoplot(as.wmppp(X))
# Test it
Ktest(X, r=seq(0.1, .5, .1))
```

*dbmss*version 2.9-0 Index]