The exponentiated exponential burr XII distribution: Theory and application to lifetime data

Article type: Research Article

Authors: Badr, Majdah M.^{; *}

Affiliations: Statistics Department, Faculty of Science for Girls, University of Jeddah, Jeddah, Saudi Arabia

Correspondence: [*] Corresponding author. Majdah M. Badr, Statistics Department, Faculty of Science for Girls, University of Jeddah, Jeddah, Saudi Arabia. E-mail: mmbadr@uj.edu.sa.

Abstract: Lifetime data collected from reliability tests are among data that often exhibit significant heterogeneity caused by variations in manufacturing which make standard lifetime models inadequate. In this paper we introduce a new lifetime distribution derived from T-X family technique called exponentiated exponential Burr XII (EE-BXII) distribution. We establish various mathematical properties. The maximum likelihood estimates (MLE) for the EE-BXII parameters are derived. We estimate the precision of the maximum likelihood estimators via simulation study. Some numerical illustrations are performed to study the behavior of the obtained estimators. Finally the model is applied to a real dataset. We apply goodness of fit statistics and graphical tools to examine the adequacy of the EE-BXII distribution. The importance of this research lies in deriving a new distribution under the name EE-BXII, which is considered the best distributions in analyzing data of life times at present if compared to many distributions in analysis real data.

Keywords: EE-BXII distribution, the maximum likelihood method, Monte Carlo simulation, variance covariance matrix

DOI: 10.3233/JIFS-200819

Journal: Journal of Intelligent & Fuzzy Systems, vol. 40, no. 3, pp. 4207-4221, 2021