derive_lq: Returns the first derivative of the quadratic Lorenz

In PIP-Technical-Team/wbpip: What the Package Does (One Line, Title Case)

Returns the first derivative of the quadratic Lorenz

Description

derive_lq() returns the first derivative of the quadratic Lorenz curves with c = 1. General quadratic form: ax^2 + bxy + cy^2 + dx + ey + f = 0. This function implements computes the derivative of equation (6b) in the original Lorenz Quadratic paper:

-(B / 2) - (\beta + 2 \alpha x) / (4 \sqrt(\alpha x^2 + \beta x + e^2)

Usage

derive_lq(x, A, B, C, key_values)

Arguments

x	numeric: Point on curve. Allow for vectors.
A	numeric: Lorenz curve coefficient. Output of regres_lq()$coef[1].
B	numeric: Lorenz curve coefficient. Output of regres_lq()$coef[2].
C	numeric: Lorenz curve coefficient. Output of regres_lq()$coef[3].
key_values	named list: key values for lq fit, calculated using A, B, C parameters using gd_lq_key_values

Value

numeric

References

Villasenor, J., B. C. Arnold. 1989. "Elliptical Lorenz curves". Journal of Econometrics 40 (2): 327-338.

PIP-Technical-Team/wbpip documentation built on Nov. 29, 2024, 6:57 a.m.