The Beta Generalized Inverse Weibull Distribution
Lamya A. Baharith *
Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia.
Salwa A Mousa
Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia and Faculty of Commerce (Girls Campus), Al-Azhar University, Cairo, Egypt.
Mahmoud A. Atallah
Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia and Faculty of Engineering, Ain Shams University, Cairo, Egypt.
Sohaila H. Elgayar
Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia and Institute of Statistical Studies and Research, Cairo University, Egypt.
*Author to whom correspondence should be addressed.
Abstract
The beta generalized inverse Weibull distribution (BGIW) is suggested in this paper. The mathematical properties of the BGIW distribution are provided and the expression for the moment generating function is derived. Also, the analytical shapes of the corresponding probability density function, reliability function, hazard rate function, and mode are derived with graphical illustrations. Expressions for the r-th positive and negative moments are calculated and the variation of the skewness and kurtosis measures is investigated. Moment and likelihood estimators of the parameters are derived. The observed information matrix is obtained. Simulation study is carried out to investigate the performance of the maximum likelihood method of estimation. Moreover, analysis of real data set is conducted to demonstrate the usefulness of the proposed distribution.
Keywords: Beta generalized inverse Weibull distribution, Fisher information matrix, moment generating function, moment estimation, maximum likelihood estimation.