quotientrule: Quotientrule

In dsfa: Distributional Stochastic Frontier Analysis

Quotientrule

Description

Quotientrule for derivs objects.

Usage

quotientrule(f_list, tri, deriv_order)

Arguments

f_list	list of derivs objects of length M, e.g. list(f_1(\cdot), f_2(\cdot),...,f_M(\cdot))
tri	list; created by the function [trind_generator()].
deriv_order	integer; maximum order of derivative. Available are 0,2 and 4.

Details

Let f_m be a function defined in [trind()], where m \in {1,...,M}. Define h((x_{n1},x_{n2},...,x_{nK})) = f_1(\cdot) / f_2(\cdot) ... / f_M(x_{n1},x_{n2},...,x_{nK})). In order to get the derivatives of h(\cdot) w.r.t all parameters x_{nk}, the quotientrule is applied. For more details see [trind()] and [trind_generator()].The values of the derivs objects must be positive. Numerically not precise, but included for reasons of completeness.

Value

Returns an object of class derivs for the function h(\cdot).

See Also

Other derivs: chainrule(), derivs_transform(), differencerule(), ind2joint(), list2derivs(), productrule(), sumrule(), trind_generator(), trind()

Examples

A<-matrix(c(1:9)/10, ncol=1)
A_derivs<-list2derivs(list(A, A^0, A^2, A^3, A^4), deriv_order=2)
B_derivs<-derivs_transform(A, type="inv", par=0,  trind_generator(1), deriv_order=2)
quotientrule (list(A_derivs, B_derivs), trind_generator(1), deriv_order=2) #A/(1/A)=A^2

dsfa documentation built on July 26, 2023, 5:51 p.m.