Alpha Logarithm-Rayleigh Distribution with Application

This manuscript introduces a novel continuous distribution referred to as the Alpha logarithm-Rayleigh distribution (AP-R), which is rooted in the alpha logarithm family. This distribution offers a fresh approach for modelling data against univariate continuous distributions. The enhancement in flexibility is accomplished by the incorporation of an extra parameter into the univariate Rayleigh distribution, facilitated by a natural logarithm transformation. The general statistical properties and moments of the new distribution were found and examined, and the maximum likelihood estimators of the two distribution parameters were found. The effectiveness of these estimators is confirmed through a Monte Carlo simulation investigation. Moreover, the application of the new distribution to two authentic datasets illustrates the advantages of the novel transformation. It is demonstrated that the proposed model surpasses the asymptotic distributions it has been juxtaposed with in the context of real data.