On the Mean Residual Life Function and Stress and Strength Analysis under Different Loss Function for Lindley Distribution

Table 1

Bayes estimator and posterior risk under different loss functions.

Loss function	Bayes estimator (BE)	Posterior risk (PR)
𝐿1=SELF=(𝜃−𝑑)^2	𝐸(𝜃∣𝐱)	Var(𝜃∣𝐱)
𝐿2()=WSELF=𝜃−𝑑^2𝜃	𝐸𝜃^−1∣𝐱^−1	𝐸(𝜃∣𝐱)−𝐸𝜃^−1∣𝐱^−1
𝐿3𝑑=𝑀/𝑄SELF=1−𝜃^2	𝐸𝜃^−1∣𝐱𝐸𝜃^−2∣𝐱	𝐸𝜃1−^−1∣𝐱^2𝐸𝜃^−2∣𝐱
𝐿4()=PLF=𝜃−𝑑^2𝑑	𝐸𝜃^2∣𝐱	2𝐸𝜃^2∣𝐱−𝐸(𝜃∣𝐱)
𝐿5=SLLF=log𝜃−log𝑑^2	exp𝐸log𝜃∣𝐱	Var log𝜃∣𝐱
𝐿6𝑑=ELF=𝜃𝑑−log𝜃−1	𝐸𝜃^−1∣𝐱^−1	Elog𝜃∣𝐱−log𝐸𝜃^−1∣𝐱
𝐿7=KLF=𝑑𝜃−𝜃𝑑^2	𝐸(𝜃∣𝐱)𝐸𝜃^−1∣𝐱	2𝐸(𝜃∣𝐱)𝐸𝜃^−1∣𝐱−1