spear_dist_distr() R function from [MSmix]

Spearman distance distribution under the uniform ranking model

Provide (either the exact or the approximate) frequency distribution of the Spearman distance under the uniform (null) ranking model.


spear_dist_distr(n_items, log = TRUE)

Arguments

n_items: Number of items.
log: Logical: whether the frequencies must be reported on the log scale. Defaults to TRUE.

Returns

A list of two named objects:

distances: All the possible Spearman distance values (i.e., the support of the distribution).
logcard: (Log)-frequencies corresponding to each value in distances.

Details

When $n\leq 20$ , the exact distribution provided by OEIS Foundation Inc. (2023) is returned by relying on a call to the get_cardinalities routine of the BayesMallows package. When $n>20$ , the approximate distribution introduced by Crispino et al. (2023) is returned. If $n>170$ , the approximation is also restricted over a fixed grid of values for the Spearman distance to limit computational burden.

Examples


## Example 1. Exact Spearman distance distribution for n=20 items.
distr <- spear_dist_distr(n_items = 20, log = FALSE)
plot(distr$distances,distr$logcard,type="l",ylab="Frequency",xlab="d",
main='Distribution of the Spearman distance\nunder the null model')

## Example 2. Approximate Spearman distance distribution for n=50 items with log-frequencies.
distr <- spear_dist_distr(n_items = 50)
plot(distr$distances,distr$logcard,type="l",ylab="Log-frequency",xlab="d",
    main='Log-distribution of the Spearman distance\nunder the null model')

References

OEIS Foundation Inc. (2023). The On-Line Encyclopedia of Integer Sequences, Published electronically at https://oeis.org.

Crispino M, Mollica C, Astuti V and Tardella L (2023). Efficient and accurate inference for mixtures of Mallows models with Spearman distance. Statistics and Computing, 33 (98), DOI: 10.1007/s11222-023-10266-8.

Sørensen Ø, Crispino M, Liu Q and Vitelli V (2020). BayesMallows: An R Package for the Bayesian Mallows Model. The R Journal, 12 (1), pages 324--342, DOI: 10.32614/RJ-2020-026.

spear_dist_distr function