Generalized Inverse Rayleigh Distribution with Applications: A Simulation Study | Chapter 3 | Mathematics and Computer Science: Contemporary Developments Vol. 3

 

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

A Study on Continuous Poisson-Rayleigh Distribution: Its Properties and Applications | Chapter 10 | Recent Advances in Mathematical Research and Computer Science Vol. 3

 The Poisson-Rayleigh distribution is a Poisson-based continuous probability distribution proposed in this article. The properties of the new distribution, such as quantile and reliability functions, and other important metrics, as well as its applications, were obtained and explored extensively in the paper. The maximum likelihood method was used to estimate the model parameters. The new distribution's utility was demonstrated empirically using real-world datasets. The Poisson-Rayleigh distribution fits the datasets far better than the Rayleigh distribution, according to the results of applying the suggested model to real-world datasets.

Author(S) Details

Abraham Iorkaa Asongo
Department of Statistics & Operations Research, MAUTech, P.M.B. 2076, Yola, Nigeria.

Innocent Boyle Eraikhuemen
Department of Physical Sciences, Benson Idahosa University Benin-City, Nigeria.

Emmanuel Remi Omoboriowo
Department of Mathematical Sciences, Gombe State University, Nigeria.

Isa Abubakar Ibrahim
Department of Mathematical & Computer Science, Federal University Kashere, Nigeria.

View Book:- https://stm.bookpi.org/RAMRCS-V3/article/view/4473

A Transmuted Power Gompertz Distribution: Properties and Applications | Chapter 11 | Theory and Practice of Mathematics and Computer Science Vol. 9

 This paper introduces and investigates the "Transmuted Power Gompertz distribution," a modern probability distribution. The new model's properties were investigated in this work. The method of maximum likelihood estimation was used to estimate the four parameters of the model. The work goes on to compare the proposed distribution's goodness-of-fit to that of other distributions by applying the model to two real-world datasets, and the results show that the proposed distribution is more stable than the fitted current distributions.

Author (s) Details

Innocent Boyle Eraikhuemen
Department of Physical Sciences, Benson Idahosa University, Benin City, Nigeria.

Terna Godfrey Ieren
Department of Statistics and Operations Research, MAUTech, P.M.B. 2076, Yola, Nigeria.

Adana’a Felix Chama
Department of Mathematical Sciences, Taraba State University, Jalingo, Nigeria.

Abraham Iorkaa Asongo
Department of Statistics and Operations Research, Modibbo Adama University of Technology (MAUTech), P.M.B. 2076, Yola, Nigeria.

Bassa Shiwaye Yakubu
Department of General Studies Education, School of General Education, Federal College of Education, Yola, Adamawa State, Nigeria.

Abdul Haruna Bala
Department of General Studies Education, School of General Education, Federal College of Education, Yola, Adamawa State, Nigeria.

View Book :- https://stm.bookpi.org/TPMCS-V9/article/view/858