. Author manuscript; available in PMC: 2017 Feb 1.

Published in final edited form as: Ann Stat. 2015 Dec 10;44(1):113–152. doi: 10.1214/15-AOS1361

Table 4.

Optimal designs for the trigonometric regression model: $f (t) = 1 + \frac{1}{2} sin (2 π t)$ , t ∈ [1, 2].

u(t)

v(t)

P_a

P_b

p(t)f(t)

(1 − π)

2π² sin(2πt)

c₁ + t

c₂ ± t

\frac{1 - π c_{1} - π}{c_{1} + 1}

\mp \frac{1 \mp π c_{2} - 2 π}{c_{2} \pm 2}

2π² sin(2πt)

t²

(2 − π)

(2π − 1)/8

2t⁻⁴((π²t²−1) sin(2πt)+πt cos(2πt)−1)

e^λt

(λ − π)e⁻^λ

πe⁻²^λ

(2π² sin(2πt) + πλcos(2πt))e⁻^λt

e^λt

e⁻^λt

(λ − π)

(λ + π)

((2π² + λ²/2) sin(2πt) + λ²)