Maximum Likelihood Estimation for an Inhomogeneous Gamma Process with a Log-linear Rate Function

Abstract An inhomogeneous gamma process is a compromise between renewal and nonhomogeneous Poisson process, since its failure probability at given time depends both on the age of system distance from last time. The with log-linear rate function often used in modelling recurrent event data. In this paper, it proved that suitably non-uniform scaled maximum likelihood estimator three-dimensional parameter model asymptotically normal, but enjoys curious property covariance matrix asymptotic distribution singular. A simulation study presented to illustrate behaviour estimators finite samples. Obtained results are also applied real data analysis.