Map \(\lambda\) to Bradley–Terry \(\theta = \lambda_i / (\lambda_i + \lambda_j)\)

Usage

lambda_to_theta(lambda)

Arguments

lambda: Numeric vector of positive rates \(\lambda_i\).

Value

A matrix with entries \(\theta_{ij} = \lambda_i / (\lambda_i + \lambda_j)\). Diagonal is 1/2 by the formula; you may overwrite if you prefer NA on the diagonal.

Examples

lambda_to_theta(c(1,2,4))
#>           [,1]      [,2]      [,3]
#> [1,] 0.5000000 0.3333333 0.2000000
#> [2,] 0.6666667 0.5000000 0.3333333
#> [3,] 0.8000000 0.6666667 0.5000000