Abstract
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.
Highlights
R ANKED set sampling (RSS) was first introduced by McIntyre [1],and Takahasi and Wakimoto [2] subsequently formulated a mathematical theory to rationalize RSS; Dell and Clutter [3] further showed that RSS is more efficient than simple random sampling (SRS)
Adatia [4] performed Bayesian estimation of a half-logistic distribution under RSS; Shaibu and Muttlak [5] performed Bayesian estimation and determined the corresponding properties for normal, exponential and gamma distributions based on RSS; an optimal linear unbiased estimation of normal and exponential distributions using RSS was performed by Sinha [6]; maximum likelihood estimation of a location-scale parameter distribution family under RSS was performed by Stokes [7]; and Bayesian estimation for a Pareto distribution under RSS was performed by Fengxi Zong and Rubing Li [8]
To our best of knowledge, little work has been done on Bayesian estimation of the log-normal distribution using ranked set samples with missing data; we investigate this subject in this paper
Summary
R ANKED set sampling (RSS) was first introduced by McIntyre [1],and Takahasi and Wakimoto [2] subsequently formulated a mathematical theory to rationalize RSS; Dell and Clutter [3] further showed that RSS is more efficient than simple random sampling (SRS). Step 1: n random samples of size n are randomly selected from the population of interest; Step 2: Each sample is ranked with respect to a variable of interest by visual inspection or any inexpensive method; Step 3: The smallest and second smallest units from the first and second samples are selected for actual measurements, and the procedure is continued until the largest unit from the nth sample is selected for measurement These three steps yield an RSS sample of size n with one cycle. To our best of knowledge, little work has been done on Bayesian estimation of the log-normal distribution using ranked set samples with missing data; we investigate this subject in this paper.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
