# PMax.Beta: Probabilities of maximization, by Beta PERT distributions In CPP: Composition of Probabilistic Preferences (CPP)

## Description

This function computes the probabilities of each alternative maximizing the preference per criterion, using Beta PERT distributions to randomize the decision matrix.

## Usage

 `1` ```PMax.Beta(x, s) ```

## Arguments

 `x` Decision matrix of Alternatives (rows) and Criteria (columns). Benefit criteria must be positive and cost criteria must be negative. `s` Shape of a Beta PERT distribution, as described in the package 'mc2d'. There is no default value, however the higher the shape the higher the kurtosis, which emulates the precision of data.

## Value

PMax are the joint probabilities of each alternative being higher than the others, per criterion.

## References

Sant'Anna, Annibal P. (2015). Probabilistic Composition of Preferences: Theory and Applications, Springer.

## Examples

 ```1 2 3 4 5 6 7 8 9``` ```# Decision matrix Alt.1 = c(2,30,86,-5) Alt.2 = c(4,26,77,-12) Alt.3 = c(3,22,93,-4) Alt.4 = c(6,34,65,-10) Alt.5 = c(5,31,80,-8) x = rbind(Alt.1,Alt.2,Alt.3,Alt.4,Alt.5) s = 4 # Shape PMax.Beta(x,s) ```

CPP documentation built on May 2, 2019, 1:34 p.m.