A three-parameter new lifetime distribution with various failure rates: Characteristics, estimation and application

In this article, we proposed a new lifetime model the so-called Slash Lindley- Rayleigh model. The new model is yielded as a ratio of 2-independent random variables, namely, a Lindley-Rayleigh model (numerator) divided by a special case of Beta distribution (denominator), specifically, an exponent to the uniform model. This proposed distribution may be theorized as stretching for a Lindley Rayleigh model, which is more flexible as concerns the kurtosis of the model. Certain important probabilistic and statistical characteristics have been founded, and the parameters of the model were estimated depending on the maximum likelihood approach. The simulation study technique has been implemented to assess the performance of the ML method by using the Monte Carlo technique. Also, real sample data of lifetimes were applied to state the usefulness and flexibility of the new model to model a positive date with surplus kurtosis.