a new generalization of the log-rayleigh probability distribution

In recent years, families of probability distributions have had useful applications in different sciences. in this paper, a new generalization of the log-rayleigh probability distribution is introduced by providing the probability density function (pdf), probability cumulative function (pcf), and some of the other main properties. then, the maximum likelihood estimation (mle) method is used to estimate the parameters of the proposed probability distribution. finally, the introduced generalized lograyleigh probability distribution is applied to calculate the initial mass function (imf) for stars.