A New Generalization of the Generalized Inverse Rayleigh Distribution with Applications

Abstract

In this article, a new four-parameter lifetime model called the beta generalized inverse Rayleigh distribution (BGIRD) is defined and studied. Mixture representation of this model is derived. Curve’s behavior of probability density function, reliability function, and hazard function are studied. Next, we derived the quantile function, median, mode, moments, harmonic mean, skewness, and kurtosis. In addition, the order statistics and the mean deviations about the mean and median are found. Other important properties including entropy (Rényi and Shannon), which is a measure of the uncertainty for this distribution, are also investigated. Maximum likelihood estimation is adopted to the model. A simulation study is conducted to estimate the parameters. Four real-life data sets from difference fields were applied on this model. In addition, a comparison between the new model and some competitive models is done via information criteria. Our model shows the best fitting for the real data.

A New Three-Parameter Inverse Rayleigh Distribution: Simulation and Application to Real Data

“…From Equation (10), it is evident that the generalized transmuted inverse Rayleigh distribution only possesses the first moment (mean). This indicates our ability to calculate the mean, but determining the variance and the higher order moments of this distribution is not possible.…”

“…In a different context, Bakoban and Al-Shehri [10] introduce the beta generalized inverse Rayleigh distribution, a four-parameter lifetime model, and conduct a comprehensive investigation into its properties and applications, further expanding the domain of inverse Rayleigh-based distributions.…”