A novel extension of generalized Rayleigh model with engineering applications

In this study, we introduce a new flexible distribution constructed by a modification to the Rayleigh distribution and we referred it as unit generalized Rayleigh distribution (UGRD). Varied statistical properties were established, such as reliability, hazard rate, survival rate, moments, quantiles, ordered statistics, etc. The maximum likelihood estimation method is applied to estimate the parameters of the proposed model and different entropy measures including: Rényi entropy, Shannon entropy, Havrda and Charvat entropy, Tsallis entropy, Arimoto entropy, and Mathai–Haubold entropy are provided. The effectiveness of the proposed entropy estimators have been conducted through Monte Carlo (MC) simulation experiments regarding average estimate, average bias, mean square error, and mean relative errors compared to the simple random sample. Finally, we illustrated two real engineering data sets to assess the potential of the proposed UGRD among some existing models.