Order statistics

Arguments

H

Object of class hyper2

...

Numeric or character vectors specifying groups of players with equal rank, with higher-ranking groups coming earlier in the argument list

all_players,winners,losers

Numeric or character vectors specifying competitors. See details

v

A character vector specifying ranks. Thus c("b","c","a") means that b came first, c second, and a third

nonfinishers

A character vector with entries corresponding to competitors who did not finish. Thus race(c("a","b"),c("p","q")) means that the field is a,b,c,d; a came first, b came second and c and d did not finish

Details

These functions are designed to return likelihood functions, in the form of lists of hyper2() objects, for typical order statistics such as the results of rowing heats or MasterChef ments.

Direct use of rankvec_likelihood() is discouraged: use suppfun() instead, for example suppfun(letters).

Function ggrl() is an easily-typed alias for general_grouped_rank_likelihood().

Function goodbad() is a convenience function for ggrl() in which a bunch of contestants is judged. It returns a likelihood function for the observation that the members of one subset were better than those of another. Thus goodbad(letters[1:3],letters[4:5]) corresponds to the observation that d and e were put into an elimination trial (and abc were not).

Function elimination() gives a likelihood function for situations where the weakest player is identified at each stage and subsequently eliminated from the competition. It is intended for situations like the Great British Bake-off and Masterchef in which the observation is which player was chosen to leave the show. In this function, argument all_players is sensitive to order, unlike choose_winners() and choose_losers() (an integer n is interpreted as letters[seq_len(n)]). Element i of all_players is the $i^\mathrm{th}$ player to be eliminated. Thus the first element of all_players is the first player to be eliminated (and would be expected to have the lowest strength). The final element of all_players is the last player to be eliminated (or alternatively the only player not to be eliminated).

Function rank_likelihood() is deprecated: use [S3 generic] supp.ranktable() instead. This takes a character vector of competitors with the order of elements corresponding to the finishing order; a Plackett-Luce likelihood function is returned. Thus v=c("d","b","c","a") corresponds to d coming first, b second, c third, and a fourth. Function race() is an arguably more memorable synonym.

An example of race() is given in inst/rowing.Rmd, and examples of ggrl() are given in inst/loser.Rmd and inst/masterchef.Rmd.

Author

Robin K. S. Hankin

See also

Examples

W <- hyper2(pnames=letters[1:5])
W1 <- ggrl(W, 'a', letters[2:4],'e')  # 6-element list
W2 <- ggrl(W, 'b', letters[3:5],'a')  # 6-element list

like_single_list(equalp(W1),W1)
#> [1] 0.05
like_series(equalp(W1),list(W1,W2))
#> [1] -5.991465

if(FALSE){  # takes too long
# run 10 races:
r1 <- rrank(10,p=(7:1)/28)
colnames(r1) <- letters[1:7]

# Likelihood function for r1:
suppfun(r1)

# convert a rank table to a support function:
suppfun(wikitable_to_ranktable(volvo_table))

H <- hyper2()
for(i in 1:20){
  H <- H + race(sample(letters[1:5],sample(3,1),replace=FALSE))
}
equalp.test(H) # should not be significant (null is true)

H1 <- hyper2(pnames=letters[1:5])
H2 <- choose_losers(H1,letters[1:4],letters[1:2])   # {a,b} vs {c,d}; {a,b} lost
maxplist(H2,control=list(maxit=1))  # control set to save time
}