\(\alpha \)-Generalized Aging Intensity Functions
We introduce a new family of generalized aging intensity functions, including the classic one as a special case (Sect. 6.1), and describe some properties of them (Sect. 6.2). We show in Sect. 6.3 that these generalized aging intensities characterize lifetime distributions. It occurs that some generalized aging intensity functions uniquely characterize single distributions, and the others characterize families of distributions dependent on scaling parameters.