On the Bayesian estimation of the weighted Lindley distribution

Abstract

The weighted distributions provide a comprehensive understanding by adding flexibility in the existing standard distributions. In this article, we considered the weighted Lindley distribution which belongs to the class of the weighted distributions and investigated various its properties. Although, our main focus is the Bayesian analysis however, stochastic ordering, the Bonferroni and the Lorenz curves, various entropies and order statistics derivations are obtained first time for the said distribution. Different types of loss functions are considered; the Bayes estimators and their respective posterior risks are computed and compared. The different reliability characteristics including hazard function, stress and strength analysis, and mean residual life function are also analysed. The Lindley approximation and the importance sampling are described for estimation of parameters. A simulation study is designed to inspect the effect of sample size on the estimated parameters. A real-life application is also presented for the illustration purpose.

Keywords:

• weighted Lindley distribution
• loss functions
• posterior risk
• failure rate function
• mean residual life function
• Lindley approximation
• importance sampling

AMS Classification:

• 62F15
• 62C10
• 62N05
• 65C60
• 62F10