On the Estimation of Parameters and Reliability Functions of a New Two-Parameter Lifetime Distribution based on Type II Censoring

Abstract

We consider here the generalization of the Bilal distribution proposed by Abd-Elrahman (2017) by zeroing in on two measures of reliability, R(t) and P, based on type II censoring. We obtain point estimators namely, λ and θ, of the above said distribution, when both parameters of the distribution are unknown. Maximum likelihood estimators (MLEs), Bayes estimators (BEs) and Lindley’s approximation for the Bayes estimators are proposed. By using independent noninformative type of priors for the unknown parameters Bayes estimators are derived. Although the proposed estimators cannot be expressed in closed forms, these can be easily obtained through the use of numerical procedures. The performance of these estimators is studied on the basis of their mean squared error (MSE), computed separately under LINEX loss function (LLF) and squared error loss function (SELF) through Monte-Carlo simulation technique.

Keywords

• maximum likelihood estimators
• bayes estimators
• non-informative prior
• lindley's approximation
• type ii censoring scheme
• squared error loss function
• linex loss function