Parameter Estimation Based on Double Ranked Set Samples with Applications to Weibull Distribution

In this paper, the likelihood function for parameter estimation based on double ranked set sampling (DRSS) schemes is introduced. The proposed likelihood function is used for the estimation of the Weibull distribution parameters. The maximum likelihood estimators (MLEs) are investigated and compared to the corresponding ones based on simple random sampling (SRS) and ranked set sampling (RSS) schemes. A Monte Carlo simulation is conducted and the absolute relative biases, mean square errors, and efficiencies are compared for the different schemes. It is found that, the MLEs based on DRSS is more efficient than MLE using SRS and RSS for estimating the two parameters of the Weibull distribution (WD).

Generalized Chain Regression-cum-Chain Ratio Estimator for Population Mean under Stratified Extreme-cum-Median Ranked Set Sampling

Estimation of population mean of study variable Y suffers loss of precision in the presence of high variation in the data set. The use of auxiliary information incorporated in construction of an estimator under ranked set sampling scheme results in efficient estimation of population mean. In this paper, we propose an efficient generalized chain regression-cum-chain ratio type estimator to estimate finite population mean of study variable under stratified extreme-cum-median ranked set sampling utilizing information on two auxiliary variables. Mean square error (MSE) of the proposed generalized estimator is derived up to first order of approximation. The applications of the proposed estimator under symmetrical and asymmetrical probability distributions are discussed using simulation study and real-life data set for comparisons of efficiency. It is concluded that the proposed generalized estimator performs efficiently as compared to some existing estimators. It is also observed that the efficiency of the proposed estimator is directly proportional to the correlations between the study variable and its auxiliary variables.

Stratified Ranked Set Sampling With Missing Observations for Estimating the Difference

The authors develop the estimation of the difference of means of a pair of variables X and Y when we deal with missing observations. A seminal paper in this line is due to Bouza and Prabhu-Ajgaonkar when the sample and the subsamples are selected using simple random sampling. In this this chapter, the authors consider the use of ranked set-sampling for estimating the difference when we deal with a stratified population. The sample error is deduced. Numerical comparisons with the classic stratified model are developed using simulated and real data.

Ratio-Type Estimation Using Scrabled Auxiliary Variables in Stratification Under Simple Random Sampling and Ranked Set Sampling

This chapter introduced basic elements on stratified simple random sampling (SSRS) on ranked set sampling (RSS). The chapter extends Singh et al. results to sampling a stratified population. The mean squared error (MSE) is derived. SRS is used independently for selecting the samples from the strata. The chapter extends Singh et al. results under the RSS design. They are used for developing the estimation in a stratified population. RSS is used for drawing the samples independently from the strata. The bias and mean squared error (MSE) of the developed estimators are derived. A comparison between the biases and MSEs obtained for the sampling designs SRS and RSS is made. Under mild conditions the comparisons sustained that each RSS model is better than its SRS alternative.

A Study of Gjestvang and Singh Randomized Response Model Using Ranked Set Sampling

In this chapter, the authors investigate the performance of the Gjestvang and Singh randomized response model for estimating the mean of a sensitive variable using ranked set sampling along the lines of Bouza. The proposed estimator is found to be unbiased, and a variance expression is derived. Then a simulation study is carried out to judge the magnitude of relative efficiency in various situations. At the end, the proposed model is assessed based on real secondary data applications. A set of SAS codes is also included.

Stratified Ranked Set Sampling (SRSS) for Estimating the Population Mean With Ratio-Type Imputation of the Missing Values

In this chapter, the authors develop stratified ranked set sampling (RSS) under missing observations. Imputation based of ratio rules is used for completing the information for estimating the mean. They introduce the needed elements on imputation and on the sample selection procedures. They extend RSS models to imputation in stratified populations. A theory on ratio-based imputation rules for estimating the mean is presented. Some numerical studies, based on real-world problems, are developed for illustrating the behaviour of the accuracy of the estimators due to their proposals.