problemdata {ClaimsProblems} | R Documentation |
Claims problem data
Description
The function returns to which of the following sub-domains the claims problem belongs to: the lower-half, higher-half, and midpoint domains. In addittion, the function returns the minimal rights vector, the truncated claims vector, the sum and the half-sum of claims.
Usage
problemdata(E, d, draw = FALSE)
Arguments
E |
The endowment. |
d |
The vector of claims. |
draw |
A logical value. |
Details
Let be the endowment to be divided and
the vector of claims
with
and such that
, the sum of claims
exceeds the endowment.
The lower-half domain is the sub-domain of claims problems for which the endowment is less or equal than the half-sum of claims, .
The higher-half domain is the sub-domain of claims problems for which the endowment is greater or equal than the half-sum of claims, .
The midpoint domain is the sub-domain of claims problems for which the endowment is equal to the half-sum of claims, .
The minimal right of claimant in
is whatever is left after every other claimant has received his claim, or 0 if that is not possible:
Let be the vector of minimal rights.
The truncated claim of claimant in
is the minimum of the claim and the endowment:
Let be the vector of truncated claims.
Value
The minimal rights vector; the truncated claims vector; the sum, the half-sum of the claims, and the class (lower-half, higher-half, and midpoint domains) to which the claims problem belongs. It returns cod = 1 if the claims problem belong to the lower-half domain, cod = -1 if it belongs to the higher-half domain, and cod = 0 for the midpoint domain. Moreover, if draw = TRUE a plot of the claims, from small to large in the interval [0,D], is given.
See Also
Examples
E=10
d=c(2,4,7,8)
problemdata(E,d,draw=TRUE)