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.
Author(s) Details
Rana Ali Bakoban
Department of Mathematics and Statistic, College of Science, University of
Jeddah, Jeddah, Saudi Arabia.
Ashwaq Mohammad
Al-Shehri
Department of Mathematics and Statistic, College of Science, University of
Jeddah, Jeddah, Saudi Arabia.
Please see the book here:- https://doi.org/10.9734/bpi/mcscd/v3/652
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