Normalizing constant function of a Mallows distribution, psi

This function calculates the normalizing constant of a Mallows distribution under the Kendall distance

psi(theta, J, R, log = FALSE)

Arguments

theta

A numeric entry specifying the Mallows scale parameter.

J

A numeric entry or vector of positive integers indicating total number of objects each judge has access to. If length(J)>1, R must be of same length or a single value.

R

A numeric entry or vector of positive integers indicating the length of the ranking provided by each judge. If length(R)>1, J must be of same length or a single value.

log

A boolean indicating if log(psi) should be returned.

Value

A numeric value or vector representing normalizing constant of a Mallows distribution.

Examples

psi(theta=1,J=10,R=8)
#> [1] 36.20464
psi(theta=2,J=c(4,4,3),R=c(2,2,1),log=TRUE)
#> [1] 0.2880096 0.2880096 0.1429316