stirling_cfa: Approximation to the binomial using Stirling's Formula

Description

Calculates the binomial aproximation using stirling's formula (Version of function: V 1.0 - November 2013)

stirling_cfa(
  observed,
  expected = NULL,
  n = sum(observed),
  p = NULL,
  cum = T,
  verb = T
)

observed: a integer vector with observed freqencies
expected: a vector giving the expected frequencies. expected can be set to expected=NULL if an vector of cell probabilities is given in argument p.
n: number of trials (scalar) default is n = sum(observed) .
p: a vector of cell probabilities. If p is not NULL the argument expected is ignored and this vector p of cell probabilities is used for calculatio instead of expected counts
cum: a logical - computation of cumulative density. If cum=TRUE (default) computes tail probability. If cum=FALSE computes prob. only for one cell (i.e. execute stircore only).
verb: logical - verbose results: If verb=TRUE (default) builds a results table. If verb=FALSE returns vector of cell p-values only.

R.W. Alexandrowicz

Vector p must be of same length as observed _or_ p may be a scalar (e.g. in case of the zero-order CFA).
The routine autoselects the upper or lower tail:
- if obs > exp then sum obs:n
- else sum 0:obs
The stirling approximation cannot be evaluated if the observed frequency is 0 or n. Therefore, the proposal of A. von Eye (20xx) is adopted, taking the sum up to 1 or n-1, respectively.

von Eye, A. (2002). Configural Frequency Analysis. Methods, Models, and Applications. Mahwah, NJ, LEA.