On Bayesian estimation from two parameter Bathtub-Shaped lifetime distribution based on progressive first-failure-censored sampling

Abstract

This paper presents different methods of Bayesian estimation to estimate parameter and reliability function of two parameter bathtub-shaped lifetime distribution based on progressively firrst-failure-censored samples under minimum expected and LINEX loss functions. Comparisons among estimators are investigated through simulation study.

Bayesian and E-Bayesian estimation for the Kumaraswamy distribution based on type-ii censoring

“…B ab  is the Bayes estimate  of given by (2-8), (2-11), (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14) and (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17). For more details see (Han [9,24]).…”

“…by using (2-17), (3)(4)(5) in (3-3) and (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17), (3)(4)(5)(6) …”

Quasi-E-Bayesian criteria versus quasi-Bayesian, quasi-hierarchical Bayesian and quasi-empirical Bayesian methods for estimating the scale parameter of the Erlang distribution

“…The quasi-hierarchical Bayes estimates of  based on DLF denoted by QHBDî The integrals in (4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20), (4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21) and (4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)…”

“…(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21) and (4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22) that…”

“…Azimi et al [19] obtained the Bayes and E-Bayes estimates for the parameter and reliability function of the generalized half Logistic distribution based on progressively type-II censored data and by considering the squared error loss and LINEX loss functions. Javadkani et al [20] constructed the Bayes, empirical Bayes and E-Bayes methods for estimating the unknown shape parameter and the reliability function of the two parameter bathtub-shaped lifetime distribution based on progressively first-failure-censoring and by considering the minimum expected loss and LINEX loss functions. Liu et al [21] obtained the E-Bayes and hierarchical estimates for the unknown parameter of the Rayleigh distribution based on q-symmetric entropy loss function in complete samples.…”