preference {HyRiM}

Decision on preferences between loss distributions

Description

This function implements the total ordering on losses, based on treating the moment sequences as hyperreal numbers, and returns the lesser of the loss distribution representatives in the hyperreal space.

Usage

preference(x, y, verbose = FALSE, weights, points = 512)

Arguments

x

a loss, being either a number,a distribution or list of distributions (objects of class mosg.lossdistribution)

y

a loss, being either a number,a distribution or list of distributions (objects of class mosg.lossdistribution)

weights

a vector of n = length(x) = length(y) nonzero numbers (not necessarily summing up to 1), used only if x and y are lists of mosg.lossdistribution objects corresponding to n>1 goals. In that case, the i-th goal gets assigend the weight (priority) weights[[i]]. Defaults to all goals having equal priority if the parameter is missing (weights = rep(1/length(x), length(x))).

verbose

if set to TRUE, the function returns the preferred of its arguments directly (thus, giving back x or y). If set to FALSE (default), then it returns the argument index (1 = x, 2 = y) or 0 in case that x=y.

points

the number of points at which the distributions are evaluated numerically to determine the preference.

Details

Deciding the preference ordering defined in terms of moment sequence as proposed in (Rass, 2015). To avoid having to compute all moments up to an unknown order, this function decides by looking at the tails of the distribution, returning the one with faster decaying tail as the preferred distribution. This method delivers exact decisions for discrete distributions, but is only an approximate approach for continous densities.

Value

the result is either a copy of the input parameter x or y, depending on which distribution is preferred.

Author(s)

Stefan Rass

References

S. Rass. On Game-Theoretic Risk Management (Part One). Towards a Theory of Games with Payoffs that are Probability-Distributions. ArXiv e-prints, June 2015. http://arxiv.org/abs/1506.07368.

See Also

lossDistribution, lossDistribution.mosg, print.mosg.lossdistribution

Examples

# use data from CVSS risk assessments
cvss1base <- c(10,6.4,9,7.9,7.1,9)
cvss2base <- c(10,7.9,8.2,7.4,10,8.5,9,9,8.7)
ld1 <- lossDistribution(cvss1base)
ld2 <- lossDistribution(cvss2base)
lowerRisk <- preference(ld1, ld2) # get the result for later use
preference(ld1, ld2, verbose=TRUE) # view the detailed answer