paircorr  R Documentation 
Estimates the paircorrelation function of a stationary RACS. The plugin moment paircorrelation estimator and three 'balanced' estimators suggested by Picka (2000) are available.
paircorr( xi, obswin = NULL, setcov_boundarythresh = NULL, estimators = "all", drop = FALSE ) paircorr.cvchat( cvchat, cpp1 = NULL, phat = NULL, estimators = "all", drop = FALSE )
xi 
An observation of a RACS of interest as a full binary map (as an 
obswin 
If 
setcov_boundarythresh 
To avoid instabilities caused by dividing by very small quantities, if the set covariance of the observation window
is smaller than 
estimators 
A list of strings specifying estimators to use.
See details.

drop 
If TRUE and one estimator selected then the returned value will be a single 
cvchat 
The plugin moment estimate of covariance as an 
cpp1 
Picka's reduced window estimate of coverage probability as an 
phat 
The plugin moment estimate of coverage probability,
which is the observed foreground area in 
The paircorrelation of a stationary RACS is
g(v) = C(v) / p^2.
The estimators available are (see (Hingee, 2019) for more information):
plugin
the plugin moment paircorrelation estimator which is Chat(v) / (phat^2), where Chat and phat are
the plugin moment estimate of covariance and the usual estimate of coverage probability, respectively.
mattfeldt
an 'intrinsically' balanced paircorrelation estimator suggested by Picka (1997).
A similar isotropic paircorrelation estimator was later studied by Mattfeldt and Stoyan (2000).
pickaint
Picka's 'intrinsically' balanced paircorrelation estimator (Picka, 2000).
pickaH
Picka's 'additively' balanced paircorrelation estimator (Picka, 2000).
If drop = TRUE
and a single estimator is requested then an
im
object containing the paircorrelation estimate is returned. Otherwise a
named imlist
of im
objects containing the paircorrelation
estimates for each requested estimator.
paircorr
: Estimates paircorrelation from a binary map.
paircorr.cvchat
: Generates paircorrelation estimates from
the plugin moment estimates of covariance, Picka's reduced window estimate of coverage probability,
and the coverage fraction (which is an unbiased estimate of the coverage probability).
If these estimates already exist then paircorr.cvchat
can save significant computation time.
Kassel Liam Hingee
Hingee, K.L. (2019) Spatial Statistics of Random Closed Sets for Earth Observations. PhD: Perth, Western Australia: University of Western Australia. Submitted.
Mattfeldt, T. and Stoyan, D. (2000) Improved estimation of the pair correlation function of random sets. Journal of Microscopy, 200, 158173.
Picka, J.D. (1997) VarianceReducing Modifications for Estimators of Dependence in Random Sets. Ph.D.: Illinois, USA: The University of Chicago.
Picka, J.D. (2000) Variance reducing modifications for estimators of standardized moments of random sets. Advances in Applied Probability, 32, 682700.
xi < as.im(heather$coarse, na.replace = 0, eps = 4 * heather$coarse$xstep) # Estimate pair correlation from a binary map pclns_directest < paircorr(xi, estimators = "all") phat < coverageprob(xi) cvchat < plugincvc(xi) cpp1 < cppicka(xi) # Compute pair correlation estimates from estimates covariance, # coverage probability and Picka's reducedwindow coverage probability. pclns_fromcvc < paircorr.cvchat(cvchat, cpp1, phat, estimators = "all")
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