Probability computation

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Description

This function computes the probability of x according to a multivariate ISR o parameter mu and pi.

Usage

1
probability(x, mu, pi, m = length(x))

Arguments

x

a vector or a matrix of 1 row containing the rankings in ranking notation (see Details or convertRank function). The rankings of each dimension are placed end to end. x must contain only full ranking (no partial or tied).

mu

a vector of length sum(m) or a matrix of size 1*sum(m), containing the modal ranks in ranking notation (see Details or convertRank function). The rankings of each dimension are placed end to end. mu must contain only full ranking (no partial or tied).

pi

a vector of size p, where p is the number of dimension, containing the probabilities of a good comparaison of the model (dispersion parameters).

m

a vector containing the size of ranks for each dimension.

Details

The ranks have to be given to the package in the ranking notation (see convertRank function), with the following convention :

- missing positions are replaced by 0

- tied are replaced by the lowest position they share"

The ranking representation r=(r_1,...,r_m) contains the ranks assigned to the objects, and means that the ith object is in r_ith position.

The ordering representation o=(o_1,...,o_m) means that object o_i is in the ith position.

Let us consider the following example to illustrate both notations: a judge, which has to rank three holidays destinations according to its preferences, O1 = Countryside, O2 =Mountain and O3 = Sea, ranks first Sea, second Countryside, and last Mountain. The ordering result of the judge is o = (3, 1, 2) whereas the ranking result is r = (2, 3, 1).

Value

the probability of x according to a multivariate ISR o parameter mu and pi.

Author(s)

Quentin Grimonprez

Examples

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m=c(4,5)
x=mu=matrix(nrow=1,ncol=9)
x[1:4] = c(1,4,2,3)
x[5:9] = c(3,5,2,4,1)
mu[1:4] = 1:4
mu[5:9] = c(3,5,4,2,1)
pi=c(0.75,0.82)

prob=probability(x,mu,pi,m)
prob