Description Usage Arguments Details Value References Examples

The unscaled envelope test, which leads to envelopes with constant width over the distances r. It corresponds to the classical maximum deviation test without scaling.

1 | ```
unscaled_envelope(curve_set, ...)
``` |

`curve_set` |
A curve_set (see |

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

This test suffers from unequal variance of T(r) over the distances r and from the asymmetry of distribution of T(r). We recommend to use the rank_envelope (if number of simulations close to 5000 can be afforded) or st_envelope/qdir_envelope (if large number of simulations cannot be afforded) instead.

An object of class "global_envelope", "envelope" and "fv" (see `fv.object`

),
which can be printed and plotted directly.

Essentially a data frame containing columns

r = the vector of values of the argument r at which the test was made

obs = values of the test function for the data point pattern

lo = the lower envelope based on the simulated functions

hi = the upper envelope based on the simulated functions

central = If the curve_set (or envelope object) contains a component 'theo', then this function is used as the central curve and returned in this component. Otherwise, the central curve is the mean of the test functions T_i(r), i=2, ..., s+1. Used for visualization only.

Additionally, the return value has attributes

method = The name of the envelope test ("Studentised envelope test" for the studentised envelope test)

alternative = "two-sided

p = A point estimate for the p-value (default is the mid-rank p-value).

u_alpha = The value of u corresponding to the 100(1-alpha)% global envelope.

u = Deviation values (u[1] is the value for the data pattern).

call = The call of the function.

and a punch of attributes for the "fv" object type.

Ripley, B.D. (1981). Spatial statistics. Wiley, New Jersey.

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 | ```
## Testing complete spatial randomness (CSR)
#-------------------------------------------
require(spatstat)
pp <- spruces
## Test for complete spatial randomness (CSR)
# Generate nsim simulations under CSR, calculate L-function for the data and simulations
env <- envelope(pp, fun="Lest", nsim=999, savefuns=TRUE, correction="translate",
simulate=expression(runifpoint(pp$n, win=pp$window)))
# The studentised envelope test
res <- unscaled_envelope(env)
plot(res)
# or (requires R library ggplot2)
plot(res, plot_style="ggplot2")
## Advanced use:
# Create a curve set, choosing the interval of distances [r_min, r_max]
curve_set <- crop_curves(env, r_min = 1, r_max = 8)
# For better visualisation, take the L(r)-r function
curve_set <- residual(curve_set, use_theo = TRUE)
# The studentised envelope test
res <- unscaled_envelope(curve_set); plot(res, plot_style="ggplot2")
## Random labeling test
#----------------------
# requires library 'marksummary'
mpp <- spruces
# Use the test function T(r) = \hat{L}_m(r), an estimator of the L_m(r) function
curve_set <- random_labelling(mpp, mtf_name = 'm', nsim=2499, r_min=1.5, r_max=9.5)
res <- unscaled_envelope(curve_set)
plot(res, plot_style="ggplot2", ylab=expression(italic(L[m](r)-L(r))))
``` |

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