Returns the first derivative of the quadratic Lorenz

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.