Abstract
This study introduces a new extended distribution of the Burr Type X distribution, using Marshall-Olkin method called the Marshall-Olkin Extended Burr Type X distribution. The new distribution is formulated by inducing a tilt parameter in the Burr Type X distribution of Marshall-Olkin, to account for the significance of the size of an event. Model parameters are obtained using maximum likelihood and Bayesian methods of estimation. The scale and shape parameters are specifically defined to identify the dimensions and density of an event. Mathematical and statistical properties and limitations of the distribution are also presented. Lifetime data analysis is performed to demonstrate the model’s applicability and flexibility. Akaike and Bayesian Information Criteria illustrate that the new distribution provides better fit compared to other distributions. This work is licensed under a Creative Commons Attribution 4.0 International License .
Highlights
Twelve different forms of distributions were introduced by Burr (1942), where the Burr Type X and Burr Type XII have gained significant interest from many researchers
The Likelihood ratio (LR) test statistics for testing the hypotheses H0: α = 1 versus H1: α ≠ 1 is Λ=146.33 (p-value < 0.05) which indicates that the Marshall Olkin extended Burr Type X (MOEBX) distribution is more suitable than Burr Type X distribution for this particular data set
The results indicate that the MOEBX distribution, in comparison with the Burr X distribution, has by far the lowest statistics of Akaike information criterion (AIC) and Bayesian information criterion (BIC) values
Summary
Twelve different forms of distributions were introduced by Burr (1942), where the Burr Type X and Burr Type XII have gained significant interest from many researchers. The single parameter distribution of the extended Burr Type X by Surles and Padgett (2001) considered as a generalized Rayleigh distribution This is characterized by normally distributed random variables with a zero mean and a constant variance, and has no correlation, and making it more applicable, instead of restricting its applicability for lifetime data.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
