# funs.pijPij: The functions for probability of selecting a number of points... In nnspat: Nearest Neighbor Methods for Spatial Patterns

 funs.pijPij R Documentation

## 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` ofpositive 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.

`pk`