Selected Ranked Set Sampling

This paper proposes a sampling procedure called selected ranked set sampling (SRSS), in which only selected observations from a ranked set sample (RSS) are measured. This paper describes the optimal linear estimation of location and scale parameters based on SRSS, and for some distributions it presents the required tables for optimal selections. For these distributions, the optimal SRSS estimators are compared with the other popular simple random sample (SRS) and RSS estimators. In every situation the estimators based on SRSS are found advantageous at least in some respect, compared to those obtained from SRS or RSS. The SRSS method with errors in ranking is also described. The relative precision of the estimator of the population mean is investigated for different degrees of correlations between the actual and erroneous ranking. The paper reports the minimum value of the correlation coefficient between the actual and the erroneous ranking required for achieving better precision with respect to the usual SRS estimator and with respect to the RSS estimator.<br /

Random sums of random vectors and multitype families of productive individuals

We prove limit theorems for a family of random vectors whose coordinates are a special form of random sums of Bernoulli random variables. Applying these limit theorems, we study the number of productive individuals in n-type indecomposable critical branching stochastic processes with types of individuals T1,…,Tn

Estimation of the population mean using random selection in ranked set samples

The use of ranked set sample to estimate the population mean is well known for its advantages over usual methods using simple random sample. In this paper we generalize the random selection in ranked set sampling proposed by Li et al. (J. Statist. Plann. Inf. 76 (1999) 185) to come up with estimator of the population mean. It will be shown that this estimator is more practical and more efficient in some cases.Normal distribution Ranked set sampling Simple random sampling