Bayesian Estimation of Log-Normal Distribution Under Ranked Set Sampling With Missing Data

In this paper, joint Bayesian estimation of two parameters of a log-normal distribution is obtained based on simple random sampling (SRS) and ranked set sampling (RSS) with complete and missing data. For the missing data case, two missing mechanisms are considered: missing at random (MAR) and missing not at random (MNAR). A logistic regression model is specified for the MNAR mechanism. The results based on SRS and RSS with three different types of prior information are compared via simulation studies with both complete and missing data. It is shown that the results obtained under RSS are significantly better than those obtained under SRS. In the simulation studies, the Gibbs sampling method, Metropolis-Hastings algorithm and importance sampling method are used to sample posterior distributions to estimate the unknown parameters of the log-normal distribution.