On the Novel Three-parameter Nakagami–Rayleigh Distribution and Its Applications

In the past few decades, numerous efforts have been made to develop a new class of lifetime distributions with greater flexibility by extending known distributions. In this paper, the two popular distributions, Nakagami and Rayleigh, were selected and combined to create a new distribution, namely the Nakagami–Rayleigh (NK-R) distribution, to obtain a distribution that was better than each other. First, its probability density and cumulative function expressions were initially derived. Then, some distributional properties such as survival function, hazard function, moment generating function, and order statistics were investigated. Next, the parameters were estimated by the maximum likelihood method, and their performance was evaluated via a simulation study with varying parameter values and sample sizes. Finally, the proposed distribution has been fitted to a real-life data set to examine its potential and flexibility. The results indicated that the offered estimators performed nicely. Furthermore, based on the Akaike information criterion, the proposed distribution provided a more appropriate model than other candidate distributions in terms of goodness of fit.