Description Usage Arguments Details Value Number of simulations References See Also Examples

The rank envelope test, p-values and global envelopes.
The test corresponds to the global envelope test that can be carriet out by
`global_envelope_test`

by specifying the `type`

for which the options
`"rank"`

, `"erl"`

, `"cont"`

and `"area"`

are available. The last
three are modifications of the first one to treat the ties in the extreme rank ordering
used in `"rank"`

. This function is kept for historical reasons.

1 | ```
rank_envelope(curve_set, type = "rank", ...)
``` |

`curve_set` |
A curve_set (see |

`type` |
The type of the global envelope with current options for "rank", "erl", "cont" and "area". If "rank", the global rank envelope accompanied by the p-interval is given (Myllymäki et al., 2017). If "erl", the global rank envelope based on extreme rank lengths accompanied by the extreme rank length p-value is given (Myllymäki et al., 2017, Mrkvička et al., 2018). See details and additional sections thereafter. |

`...` |
Additional parameters to be passed to |

The `"rank"`

envelope test is a completely non-parametric test, which provides
the 100(1-alpha)% global envelope for the chosen test function T(r) on
the chosen interval of distances and associated p-values.
The other three types are solutions to break the ties in the extreme ranks
on which the `"rank"`

envelope test is based on.

Note: The method to break ties for the global `type = "rank"`

envelope
(Myllymäki et al., 2017) can be done by the argument `ties`

with default
to `ties = "erl"`

corresponding to the extreme rank length breaking of ties.
In this case the global envelope corresponds to the extreme rank measure.
If instead choosing `type`

to be `"erl"`

, `"cont"`

or `"area"`

,
then the global envelope corresponds to these measures.

An object of class `global_envelope`

of `combined_global_envelope`

which can be printed and plotted directly. See `global_envelope_test`

for more details.

The global `"erl"`

, `"cont"`

, `"area"`

envelope tests allow
in principle a lower number of simulations to be used than the global `"rank"`

test
based on extreme ranks.
However, if feasible, we recommend some thousands of simulations in any case to achieve
a good power and repeatability of the test.
For the global `"rank"`

envelope test, Myllymäki et al. (2017) recommended to use
at least 2500 simulations for testing at the significance level alpha = 0.05 for single
function tests, experimented with summary functions for point processes.

Myllymäki, M., Mrkvička, T., Grabarnik, P., Seijo, H. and Hahn, U. (2017). Global envelope tests for spatial point patterns. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 79: 381–404. doi: 10.1111/rssb.12172

Mrkvička, T., Myllymäki, M. and Hahn, U. (2017). Multiple Monte Carlo testing, with applications in spatial point processes. Statistics & Computing 27 (5): 1239-1255. doi: 10.1007/s11222-016-9683-9

Mrkvička, T., Myllymäki, M., Jilek, M. and Hahn, U. (2020) A one-way ANOVA test for functional data with graphical interpretation. Kybernetika 56 (3), 432-458. doi: 10.14736/kyb-2020-3-0432

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 | ```
# See ?global_envelope_test for more examples
## Testing complete spatial randomness (CSR)
#-------------------------------------------
if(require("spatstat.core", quietly=TRUE)) {
X <- unmark(spruces)
nsim <- 2499 # Number of simulations
# Generate nsim simulations under CSR, calculate centred L-function for the data and simulations
env <- envelope(X, fun="Lest", nsim=nsim, savefuns=TRUE,
correction="translate", transform=expression(.-r),
simulate=expression(runifpoint(ex=X)))
# The rank envelope test
res <- rank_envelope(env)
# Plot the result.
plot(res)
## Advanced use:
# Choose the interval of distances [r_min, r_max] (at the same time create a curve_set from 'env')
curve_set <- crop_curves(env, r_min=1, r_max=7)
# Do the rank envelope test
res <- rank_envelope(curve_set); plot(res)
}
``` |

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