preference | R Documentation |
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.
preference(x, y, verbose = FALSE, weights, points = 512)
x |
a loss, being either a number,a distribution or list of distributions (objects of class |
y |
a loss, being either a number,a distribution or list of distributions (objects of class |
weights |
a vector of |
verbose |
if set to |
points |
the number of points at which the distributions are evaluated numerically to determine the preference. |
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.
the result is either a copy of the input parameter x
or y
, depending on which distribution is preferred.
Stefan Rass
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.
lossDistribution
, lossDistribution.mosg
, print.mosg.lossdistribution
# 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
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