Length Biased Burr-III Distribution for Modeling the Glass and Carbon Fiber Strength
M. M. E. Abd El-Monsef *
Faculty of Science, Tanta University, Tanta, Egypt.
S. A. Desoky
Faculty of Science, Tanta University, Tanta, Egypt.
W. A. Hassanein
Faculty of Science, Tanta University, Tanta, Egypt.
*Author to whom correspondence should be addressed.
Abstract
This paper introduces the length-biased Burr III (LBBIII) distribution, derived by applying a length-biased weighting scheme to the standard two-parameter Burr III distribution. The model is particularly suitable for lifetime and strength data, where the probability of observing an event is proportional to its magnitude. Most of its statistical and reliability properties were derived. Four estimation methods are examined and a simulation study evaluates the finite-sample performance of these estimators. The practical utility of the LBBIII distribution is demonstrated using two real datasets on glass and carbon fiber strength. The proposed distribution consistently outperforms the standard Burr-III and some well-known distributions. These findings establish the LBBIII distribution as a flexible and superior model for length-biased reliability and strength data.
Keywords: Burr III distribution, length biased, survival function, order statistics, maximum likelihood method