A new three-parameter lifetime distribution called the Topp-Leone generalized Rayleigh (TLGR) distribution obtained by the Topp-Leone generator based on the generalized Rayleigh (GR) distribution is proposed. Some of the proposed distribution’s mathematical properties such as its survival function, hazard function, moments, and moment generating function are investigated. Furthermore, the expansion of the probability density function is derived in terms of a linear combination of the GR distribution; this function is used to obtain its moments, and the maximum likelihood method is applied to estimate its parameters. Using real-life datasets, a comparative analysis is carried out to fit them to the TLGR, GR, and Rayleigh distributions based on the Anderson-Darling test and the Akaike information and Bayesian information criteria. The results from these datasets exhibit that the TLGR distribution is more appropriate than the other distributions.
