In this paper, a new framework for generating lifetime distributions is introduced, called the Topp-Leone generated (TLG) family of distributions. The generator of the TLG family is the Topp-Leone distribution, which was proposed by Topp and Leone in 1955. Some various properties of the TLG distribution are discussed, e.g., survival function, hazard function, moments and generating function. In addition, the TLG family is capable of improving fitted results and tail behavior of existing distributions. We present the Topp-Leone generalized exponential (TLGE) distribution as an example of the TLG distribution. Some graphical representations related to the probability density function and hazard function of the TLGE distribution are provided. In application study, the goodness of fit test based on the TLGE, the generalized exponential (GE), and exponentiated generalized exponential (EGE) distributions are compared. The results emphasize that the TLGE distribution can be considered as a competitive distribution for the GE and EGE distributions.
