fullcable.t: Evaluate Bent Cable Function

In bentcableAR: Bent-Cable Regression for Independent Data or Autoregressive Time Series

Evaluate Bent Cable Function

Description

The bent-cable response is evaluated at a provided design point t.

Usage

fullcable.t(t, b0, b1, b2, tau, gamma)

Arguments

t	A design point at which the bent cable is to be evaluated.
b0	Intercept.
b1	Incoming slope.
b2	Coefficient of the basic bent cable.
tau	Centre of the quadratic bend (transition).
gamma	Non-negative half-width of the quadratic bend.

Details

All arguments must be numeric, and at most one can be a vector.

The full bent cable has the form f(t) = b_0 + b_1 t + b_2 q(t), where q(t) is the basic bent cable function with intercept and slope 0 and outgoing slope 1:

q(t)=\frac{(t-τ+γ)^2}{4γ} I\{|t-τ|≤qγ\} + (t-τ) I\{t>τ+γ\}

for γ≥q 0.

Note

This function is intended for internal use by bentcable.ar and bentcable.dev.plot.

Author(s)

Grace Chiu

References

See the bentcableAR package references.

Examples

	# basic broken stick, kink at 0:
	plot( seq(-10,10), fullcable.t(seq(-10,10),0,0,1,0,0) )
	
	# full bent cable, bend centred at 0 with half-width 3:
	plot( seq(-10,10), fullcable.t(seq(-10,10),1,.1,-.5,0,3) )

bentcableAR documentation built on June 28, 2022, 5:05 p.m.