funs.pijPij {nnspat}

The functions for probability of selecting a number of points from respective classes

Description

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.

Usage

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)

Arguments

k, l, m, p

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.

n

A positive integer representing the size of the data set (i.e., number of observations in the data set).

nvec

A vector of positive integers representing the sizes of classes in the data set, used in Pij type functions only.

Value

Probability values for the selected points being from the indicated classes.

See Also

pk