Bayesian Analysis of Weibull-Lindley Distribution Using Different Loss Functions
Innocent Boyle Eraikhuemen *
Department of Physical Sciences, Benson Idahosa University, Benin-City, Nigeria.
Olateju Alao Bamigbala
Department of Mathematics and Statistics, Federal University Wukari, Taraba State, Nigeria.
Umar Alhaji Magaji
Department of Mathematics, Jigawa State College of Education, Gumel, Jigawa State, Nigeria.
Bassa Shiwaye Yakura
Department of General Studies, School of General Education, Federal College of Education, Yola, Adamawa State, Nigeria.
Kabiru Ahmed Manju
Department of General Studies, School of General Education, Federal College of Education, Yola, Adamawa State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
In the present paper, a three-parameter Weibull-Lindley distribution is considered for Bayesian analysis. The estimation of a shape parameter of Weibull-Lindley distribution is obtained with the help of both the classical and Bayesian methods. Bayesian estimators are obtained by using Jeffrey’s prior, uniform prior and Gamma prior under square error loss function, quadratic loss function and Precautionary loss function. Estimation by the method of Maximum likelihood is also discussed. These methods are compared by using mean square error through simulation study with varying parameter values and sample sizes.
Keywords: Weibull-Lindley distribution, Bayesian method, priors, loss functions, MLE, simulation, MSE.