Transmuted Burr Type X Distribution with Covariates Regression Modeling to Analyze Reliability Data

SYNOPTIC ABSTRACT

This article investigates the potential usefulness of the three-parameter transmuted Burr type X (TBX) distribution for modeling reliability data, and explore its structural properties using simulation. Explicit expressions are derived for moments, incomplete moments, entropies, and mean deviation. The method of maximum likelihood is used for estimating the model parameters. We conduct Monte Carlo simulations, which are used to examine the relative performance of the estimators using MLE in terms of bias and mean square errors. A location-scale regression model based on the log-TBX distribution is proposed for modeling lifetime data. Use of this family of distributions is illustrated for fatigue fracture data and multiple myeloma patient’s data.

KEYWORDS AND PHRASES:

• Log-transmuted Burr Type X distribution
• maximum likelihood estimation
• moment estimation
• statistical computing

Acknowledgements

The authors would like to thank the reviewers for their constructive comments and suggestions, and especially appreciated the Editor-in-Chief for their valuable comments, which improved the quality and presentation of this article.