Thomae: Maximum Excess Representation of a Generalized Hypergeometric Function Using Thomae's Theorem

Description

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.

Usage

ULg(U, L)
combiopt(g)
Thomae(U, L, lB, tol, maxiter, debug)
gb2.gini(shape1, shape2, shape3, tol=1e-08, maxiter=10000, debug=FALSE)

Arguments

vector of length 3 giving the upper arguments of the generalized hypergeometric function $_{3}F_{2}$.

vector of length 2 giving the lower arguments of the generalized hypergeometric function $_{3}F_{2}$.

vector of Thomae's permuting arguments.

ratio of beta functions (a common factor in the expression of the Gini coefficient under the GB2).

shape1

positive parameter.

shape2, shape3

positive parameters of the Beta distribution.

tol

tolerance with default 0, meaning to iterate until additional terms do not change the partial sum.

maxiter

maximum number of iterations to perform.

debug

boolean; if TRUE, returns the list of changes to the partial sum.

Value

ULg returns a list containing Thomae's arguments and the excess, combiopt gives the optimal combination of Thomae's arguments (for internal use only), Thomae returns the optimal representation of the $_{3}F_{2}(U,L;1)$, GB2.Gini returns the Gini coefficient under the GB2.

Details

More details can be found in Graf (2009).

References