Simulation Study of the Bayesian and Non-Bayesian Estimation of a new Lifetime Distribution Parameters with Increasing Hazard Rate
Dorathy O. Oramulu
Department of Statistics, Faculty of Physical Sciences, Nnamdi Azikiwe University, Awka, Nigeria.
Chinyere P. Igbokwe
Department of Statistics, Abia State Polytechnic, Aba, Nigeria.
Ifeanyi C. Anabike
Department of Statistics, Faculty of Physical Sciences, Nnamdi Azikiwe University, Awka, Nigeria.
Harrison O. Etaga
Department of Statistics, Faculty of Physical Sciences, Nnamdi Azikiwe University, Awka, Nigeria.
Okechukwu J. Obulezi *
Department of Statistics, Faculty of Physical Sciences, Nnamdi Azikiwe University, Awka, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
In this paper, a new distribution known as the Shifted Chris-Jerry (SHCJ) distribution is proposed. The proposition is motivated by the need to compare the efficiency of various classical estimation methods as well as the bayesian estimation using gamma prior at linear-exponential loss, squared error loss and generalized entropy loss functions. Some useful mathematical properties are derived. Single acceptance sampling plans (SASPs) are created for the distribution when the life test is truncated at a predetermined period. The median lifetime of the SHCJ distribution with pre-defined constants is taken as the truncation time. To guarantee that the specific life test is obtained at the defined risk to the user, the minimum sample size is required. For a particular consumer’s risk, the SHCJ distribution’s parameters, and the truncation time including numerical results are obtained. A simulation study is carried out for the bayesian and non-bayesian estimation of the parameters. Data on blood cancer patients is used to demonstrate the usefuleness of the proposed distribution.
Keywords: Acceptance sampling, Chris-Jerry distribution, estimation, shifted Chris-Jerry distribution