Random hyper3 objects

Various random hyper3 objects, in the context of the race metaphor. They return “get you going” examples of hyper3 objects. The defaults correspond to simple but non-trivial with straightforward interpretations.

The defaults are



 pn: c(a=2,   b=4,   c=2,   d=1  )  # numbers (two "a"s, four "b"s etc)
 ps: c(a=0.3, b=0.1, c=0.2, d=0.4)  # strengths
rwinner3(pn = c(a=2, b=4, c=2, d=1), ps = c(a=0.3, b=0.1, c=0.2, d=0.4))
rpair3(n=5, s=3, lambda=1.3)
rrace3(pn = c(a=2, b=4, c=2, d=1), ps=c(a=0.3, b=0.1, c=0.2, d=0.4))
rracehyper3(n=4, size=9, ps=NULL, races=3)
rhyper3(n=5, s=4, type='race', ...)

Arguments

pn

A named integer vector showing numbers of each type of player

ps

A named vector showing strengths of each type of player

n,size,races,s,type

Arguments specifying the complexity of the random hyper3 object returned. See details

lambda

Parameter

...

Further arguments passed to rracehyper3() or rpair3()

Details

These functions return hyper3 objects, as indicated by the 3 in their names.

  • Function rwinner3() is a low-level helper function that takes a player number argument pn, and a player strength argument ps. It performs an in silico race, and returns the (name of) the winner, chosen randomly from a field of runners with appropriate strengths. It is used repeatedly by rrace3() to select a winner from the diminishing pool of still-running players.

  • Function rpair3() returns a hyper3 object corresponding to repeated pairwise comparisons including a white-player advantage represented by lambda.

  • Function rrace3() returns a rank statistic corresponding to finishing order for a Plackett-Luce race. The output can be passed to ordervec2supp3().

  • Function rracehyper3() returns a more complicated hyper3 object corresponding to repeated races.

  • Function rhyper3() returns an even more complicated hyper3 object corresponding to repeated races and pairwise comparisons.

Argument n generally specifies the number of distinct types of players. Files inst/mann_whitney_wilcoxon.Rmd and inst/javelin.Rmd show some use-cases for these functions.

Author

Robin K. S. Hankin

Note

In function rracehyper3() [and by extension rhyper3()], if argument n exceeds 26 and argument pn takes its default value of NULL, then an error will be returned because there are only 26 players, one for each letter a-z.

Examples


rracehyper3()
#> log( (a=1)^9 * (a=1, b=1)^-1 * (a=1, b=1, c=1)^-2 * (a=1, b=1, c=2)^-1
#> * (a=1, b=1, c=3)^-1 * (a=1, b=2, c=1)^-1 * (a=1, b=2, c=2)^-1 * (a=1,
#> b=2, c=3)^-2 * (a=1, b=3, c=3)^-1 * (a=2, b=1, c=2)^-1 * (a=2, b=1,
#> c=3)^-1 * (a=2, b=2, c=3)^-2 * (a=2, b=3, c=3)^-2 * (a=3, b=2, c=3)^-1
#> * (a=3, b=3, c=3)^-3 * (b=1)^8 * (b=1, c=1)^-1 * (b=1, c=3)^-1 *
#> (c=1)^7 * (c=2)^-1 * (c=3)^-1)
rrace3()
#> [1] "d" "a" "c" "c" "a" "b" "b" "b" "b"
rwinner3()
#> [1] "a"
rhyper3()
#> log( (a=1)^3 * (a=1, c=1, e=2)^-3 * (c=1)^2 * (c=1, e=1)^-2 * (c=1,
#> e=2)^-3 * (e=1)^4 * (e=2)^-1)
rpair3()
#> log( (a=1.3)^1 * (a=1.3, d=1)^-1 * (b=1.3)^1 * (b=1.3, d=1)^-1 *
#> (c=1.3)^1 * (c=1.3, e=1)^-1)
ordervec2supp3(rrace3())
#> log( (a=1)^2 * (a=1, b=2, c=1, d=1)^-1 * (a=1, b=3, c=1, d=1)^-1 *
#> (a=2, b=3, c=1, d=1)^-1 * (a=2, b=3, c=2, d=1)^-1 * (a=2, b=4, c=2,
#> d=1)^-1 * (b=1)^3 * (b=1, d=1)^-1 * (b=2, c=1, d=1)^-1 * (b=2, d=1)^-1
#> * (c=1)^2 * (d=1)^1)

table(replicate(100,which(rrace3(pn=c(a=1,b=10),ps=c(a=0.9,b=0.1))=='a')))
#> 
#>  1  2  3  4  5  6  7 
#> 51 25 11  8  2  1  2