mono_cns: Monotonicity constraint for the quantile function

In thomasblanchet/gpinter: Generalized Pareto Interpolation

Monotonicity constraint for the quantile function

Description

This set of functions provide constraints on the parameters of the quintic spline that ensure an increasing quantile function. The function mono_cns returns nine values that must all be non-negative. The other are the derivatives of those constraints with respect to each parameters. Those conditions were derived using the Bernstein polynomial form of the constraint (see Mathematica workbook for details).

Usage

mono_cns(x0, x1, y0, y1, s0, s1, a0, a1)

Arguments

x0	Lower bound of the interval.
x1	Upper bound of the interval.
y0	Value of the spline at x0.
y1	Value of the spline at x1.
s0	Slope of the spline at x0.
s1	Slope of the spline at x1.
a0	Second derivative of the spline at x0.
a1	Second derivative of the spline at x1.

Value

The value of the nine constraints or their derivative.

Author(s)

Thomas Blanchet, Juliette Fournier, Thomas Piketty

thomasblanchet/gpinter documentation built on Nov. 29, 2022, 4:32 a.m.