Expected value of metrics under a Mallows rank model

Compute the expectation of several metrics under the Mallows rank model.

Usage

compute_expected_distance(
  alpha,
  n_items,
  metric = c("footrule", "spearman", "cayley", "hamming", "kendall", "ulam")
)

Arguments

alpha

Non-negative scalar specifying the scale (precision) parameter in the Mallows rank model.

n_items

Integer specifying the number of items.

metric

Character string specifying the distance measure to use. Available options are "kendall", "cayley", "hamming", "ulam", "footrule", and "spearman".

Value

A scalar providing the expected value of the metric under the Mallows rank model with distance specified by the metric argument.

See also

Other rank functions: compute_observation_frequency(), compute_rank_distance(), create_ranking(), get_mallows_loglik(), sample_mallows()

Examples

compute_expected_distance(1, 5, metric = "kendall")
#> [1] 4.177277
compute_expected_distance(2, 6, metric = "cayley")
#> [1] 3.212053
compute_expected_distance(1.5, 7, metric = "hamming")
#> [1] 5.761023
compute_expected_distance(5, 30, "ulam")
#> [1] 21.33016
compute_expected_distance(3.5, 45, "footrule")
#> [1] 377.5987
compute_expected_distance(4, 10, "spearman")
#> [1] 7.220669