The function returns which of the following subdomains 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.
problemdata(E, d, draw = FALSE)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.
The endowment.
The vector of claims.
A logical value.
Let \(N=\{1,\ldots,n\}\) be the set of claimants, \(E\ge 0\) the endowment to be divided and \(d\in \mathbb{R}_+^N\) the vector of claims such that \(D=\sum_{i \in N} d_i\ge E\).
The lower-half domain is the subdomain of claims problems for which the endowment is less or equal than the half-sum of claims, \(E \le D/2\).
The higher-half domain is the subdomain of claims problems for which the endowment is greater or equal than the half-sum of claims, \(E \ge D/2\).
The midpoint domain is the subdomain of claims problems for which the endowment is equal to the half-sum of claims, \(E = D/2\).
The minimal right of claimant \(i\in N\) in \((E,d)\) is whatever is left after every other claimant has received his claim, or 0 if that is not possible: $$m_i(E,d)=\max\{0,E-d(N\backslash\{i\})\}.$$ Let \(m(E,d)=\Bigl(m_1(E,d),\dots,m_n(E,d)\Bigr)\) be the vector of minimal rights.
The truncated claim of claimant \(i\in N\) in \((E,d)\) is the minimum of the claim and the endowment: $$t_i(E,d)=\min\{d_i,E\}.$$ Let \(t(E,d)=\Bigl(t_1(E,d),\dots,t_n(E,d)\Bigr)\) be the vector of truncated claims.
allrules, setofawards.
E=10
d=c(2,4,7,8)
problemdata(E,d,draw=TRUE)
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