TY - JOUR

T1 - Building a statistical model to predict reactor temperatures.

AU - Scarrott, Carl J.

AU - Tunnicliffe Wilson, Granville

PY - 2001

Y1 - 2001

N2 - We investigate the monotonicity of various averages of the values of a convex (or concave) function at n equally spaced points. For a convex function, averages without end points increase with n, while averages with end points decrease. Averages including one end point are treated as a special case of upper and lower Riemann sums, which are shown to decrease and increase, respectively. Corresponding results for mid-point Riemann sums and the trapezium estimate require convexity or concavity of the derivative as well as the function. Special cases include some known results and some new ones, unifying them in a more systematic theory. Further applications include results on series and power majorization.

AB - We investigate the monotonicity of various averages of the values of a convex (or concave) function at n equally spaced points. For a convex function, averages without end points increase with n, while averages with end points decrease. Averages including one end point are treated as a special case of upper and lower Riemann sums, which are shown to decrease and increase, respectively. Corresponding results for mid-point Riemann sums and the trapezium estimate require convexity or concavity of the derivative as well as the function. Special cases include some known results and some new ones, unifying them in a more systematic theory. Further applications include results on series and power majorization.

U2 - 10.1080/02664760120034207

DO - 10.1080/02664760120034207

M3 - Journal article

VL - 28

SP - 497

EP - 504

JO - Journal of Applied Statistics

JF - Journal of Applied Statistics

SN - 1360-0532

IS - 3-4

ER -