Defines Thomae's arguments from the upper (U) and lower (L) parameters of a \(_{3}F_{2}(U,L;1)\). Computes the optimal combination leading to the maximum excess.
Computes the optimal combination of Thomae's arguments and calculates the optimal representation of the \(_{3}F_{2}(U,L;1)\) using the genhypergeo_series function from package hypergeo.
Computes the Gini coefficient for the GB2 distribution, using Thomae's theorem.
ULg(U, L)
combiopt(g)
Thomae(U, L, lB, tol, maxiter, debug)
gb2.gini(shape1, shape2, shape3, tol=1e-08, maxiter=10000, debug=FALSE)numeric; vector of length 3 giving the upper arguments of the generalized hypergeometric function \(_{3}F_{2}\).
numeric; vector of length 2 giving the lower arguments of the generalized hypergeometric function \(_{3}F_{2}\).
numeric; vector of Thomae's permuting arguments.
numeric; ratio of beta functions (a common factor in the expression of the Gini coefficient under the GB2).
numeric; positive parameter.
numeric; positive parameters of the Beta distribution.
numeric; tolerance with default 0, meaning to iterate until additional terms do not change the partial sum.
numeric; maximum number of iterations to perform.
boolean; if TRUE, returns the list of changes to the partial sum.
ULg returns a list containing Thomae's arguments and the excess, combiopt gives the optimal combination of Thomae's arguments,
Thomae returns the optimal representation of the \(_{3}F_{2}(U,L;1)\), gb2.gini returns the value of the Gini coefficient under the GB2.
Internal use only. More details can be found in Graf (2009).
Graf, M. (2009) An Efficient Algorithm for the Computation of the Gini coefficient of the Generalized Beta Distribution of the Second Kind. ASA Proceedings of the Joint Statistical Meetings, 4835--4843. American Statistical Association (Alexandria, VA).
McDonald, J. B. (1984) Some generalized functions for the size distribution of income. Econometrica, 52, 647--663.