Confidence intervals for the scale parameter of the power-law process

Olivier Gaudoin (1) , Bo Yang (2) , Min Xie (3)

1 LMC - IMAG - Laboratoire de Modélisation et Calcul
2 UESTC - University of Electronic Science and Technology of China [Chengdu]
3 NUS - National University of Singapore

The Power-Law Process (PLP) is a two-parameter model widely used for modeling repairable system reliability. Results on exact point estimation for both parameters as well as exact interval estimation for the shape parameter are well-known. In this paper, we investigate the interval estimation for the scale parameter. Asymptotic confidence intervals are derived using Fisher information matrix and theoretical results by Cocozza-Thivent (1997). The accuracy of the interval estimation for finite samples is studied by simulation methods.

Mots clés: Asymptotic confidence interval; Information matrix; Maximum likelihood estimation; Nonhomogeneous Poisson process; Power-law process; Repairable system reliability

Domaines: Statistiques [math.ST]

Olivier Gaudoin, Bo Yang, Min Xie. Confidence intervals for the scale parameter of the power-law process. Communications in Statistics - Theory and Methods, 2006, 35 (8), pp.1525-1538. ⟨10.1080/03610920600637412⟩. ⟨hal-00305803⟩