Best efficient estimates of the intensity function of the power law process

We develop a general statistical procedure to obtain linearly the best efficient estimate of existing estimations of the parameter of a probability process. This procedure is used to obtain the best efficient estimates of the shape parameter, the intensity failure function and its reciprocal of the power law process. These estimates are important in the study of reliability growth modelling. The effectiveness of our findings is illustrated analytically and numerically, using real data and numerical simulations.