A New Family of Extended Rayleigh Distribution: Properties and Estimation

الملخص

   This paper presents a new type of continuous family distribution constructed on the truncated Rayleigh-Rayleigh distribution [0,1]. This distribution addresses the challenges posed by increasing data complexity, particularly in failure modeling, where it provides a suitable alternative when the normal distribution is inadequate. Using the maximum likelihood method (MLE) for parameter estimation, simulations were conducted to experimentally determine the behavior of the TR-RD parameters with different sample sizes (n = 10, 20, 50, 100) and (200, 300,400,500). The simulation results demonstrated that using small parameter values ​​with large sample sizes yields a clear advantage, achieving the lowest mean squared error (MSE). This paper also defines several properties of this distribution, including, for example, the r-order moment function, the reliability function, the failure rate function, the dielectric strength function, and the Shannon entropy function.