Generalized Inverse Rayleigh Distribution with Applications: A Simulation Study

In this article, a new four-parameter lifetime model called the beta generalized inverse Rayleigh distribution (BGIRD) is defined and studied. This paper proposes a solution by introducing a new two-parameter extension of this distribution through the use of beta generator distribution. A 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. The model uses maximum likelihood estimation. Estimation research using simulation is carried out. In this model, five real-world data sets from various disciplines were applied. Additionally, information criteria are used to compare the new model with a few rival models. Our model shows the best fitting for the real data. Maximum likelihood estimators of the BGIRD parameters are obtained. Simulation studies of Monte Carlo are conducted under various sample sizes to study the theoretical performance of the MLE of the parameters. Five real data sets are analyzed and a good fit for the data sets has been provided by the BGIRD.