Statistical inference for the Nadarajah-Haghighi distribution based on ranked set sampling with applications

Abstract

In this article, the maximum likelihood and Bayes inference methods are discussed for determining the two unknown parameters and specific lifetime parameters of the Nadarajah-Haghighi distribution, such as the survival and hazard rate functions, with the inclusion of ranked set sampling and simple random sampling. The estimated confidence intervals for the two parameters and any function of them are developed based on the Fisher-information matrix. Metropolis-Hastings algorithm and Lindley-approximation are used for generating the Bayes estimates and related highest posterior density credible ranges for the unknown parameters and reliability parameters under the presumption of conjugate gamma priors. A Monte-Carlo simulation study and a real-life data set have been used to assess the efficacy of the proposed methods.

Keywords

• ranked set sampling
• nadarajah-haghighi distribution
• maximum likelihood estimation
• lindley approximation method
• metropolis-hastings algorithm