The ancillary probability functions used in computation of
the variance-covariance matrices
of various NN spatial tests such as NNCT tests and
tests based on other contingency tables.
These functions can be classified as pij
and Pij type functions.
The pij functions are for individual
probabilities and the corresponding Pij functions are
the summed pij values.
For example \(p_{iijk}\)
is the probability of any 4 points with 2 from class \(i\),
and others are from classes \(j\) and \(k\).
These probabilities are for data from RL or CSR.
p11(k, n)P11(nvec)
p12(k, l, n)
P12(nvec)
p111(k, n)
P111(nvec)
p1111(k, n)
P1111(nvec)
p112(k, l, n)
P112(nvec)
p122(k, l, n)
p123(k, l, m, n)
P123(nvec)
p1234(k, l, m, p, n)
P1234(nvec)
p1223(k, l, m, n)
p1123(k, l, m, n)
P1123(nvec)
p1122(k, l, n)
P1122(nvec)
p1112(k, l, n)
P1112(nvec)
Probability values for the selected points being from the indicated classes.
Positive integers, usually representing the class sizes,
used in pij type functions only.
Number of these arguments required depends on the number of
distinct indices of \(p\), e.g. \(p_{ij}\) requires
k,l,n and \(p_{iijk}\) requires k,l,m,n as input.
A positive integer representing the size of the data set (i.e., number of observations in the data set).
A vector of positive integers representing
the sizes of classes in the data set, used in
Pij type functions only.
pk