LCAextend (version 1.3)

alpha.compute: computes cumulative logistic coefficients using probabilities

Description

computes cumulative logistic coefficients using probabilities.

Usage

alpha.compute(p)

Arguments

p

a vector of probabilities (positive entries summing to 1).

Value

The function returns alpha: a vector of S-1 cumulative logistic coefficients.

Details

If p has one value (equal to 1) alpha.compute returns NA, if it has S (S>=2) values, alpha.compute returns S-1 coefficients alpha such that if Y is a random variable taking values in {1,...,S} with probabilities p, coefficients alpha[i] are given by:

$$ p_1+...+p_i=P(Y\leq i)=\frac{\exp(\alpha_1+...+\alpha_i)}{1+\exp(\alpha_1+...+\alpha_i)}, $$

for all i<=S-1.

See Also

alpha.compute is the inverse function of p.compute

Examples

# NOT RUN {
# a vector of probability
p <- c(0,0.2,0,0,0.3,0.4,0.1,0,0)
alpha.compute(p)
#gives -Inf -1.38 0 0 1.38 0 2.19 Inf Inf
p.compute(alpha.compute(rep(1/5,5)))
# }