Half logistic exponentiated inverse Rayleigh distribution: Properties and application to life time data

This paper presents a novel extension of the exponentiated inverse Rayleigh distribution called the half-logistic exponentiated inverse Rayleigh distribution. This extension improves the flexibility of the distribution for modeling lifetime data for both monotonic and non-monotonic hazard rates. The statistical properties of the half-logistic exponentiated inverse Rayleigh distribution, such as the quantiles, moments, reliability, and hazard function, are examined. In particular, we provide several techniques to estimate the half-logistic exponentiated inverse Rayleigh distribution parameters: weighted least squares, Cramér-Von Mises, maximum likelihood, maximum product spacings and ordinary least squares methods. Moreover, numerical simulations were performed to evaluate these estimation methods for both small and large samples through Monte Carlo simulations, and the finding reveals that the maximum likelihood estimation was the best among all estimation methods since it comprises small mean square error compared to other estimation methods. We employ real-world lifetime data to demonstrate the performance of the newly generated distribution compared to other distributions through practical application. The results show that the half-logistic exponentiated inverse Rayleigh distribution performs better than alternative versions of the Rayleigh distributions.