Bivariate Ranked Set Sampling Research Articles

Clustering and estimation of finite mixture models under bivariate ranked set sampling with application to a breast cancer study

Clustering and estimation of finite mixture models under bivariate ranked set sampling with application to a breast cancer study

Ranked set sampling in finite populations with bivariate responses: An application to an osteoporosis study.

The majority of the research on rank-based sampling designs in finite populations has been concerned with univariate situations. In this article, we study design-based estimation using a bivariate ranked set sampling (BIRSS) for finite populations when we have bivariate response variables. We derive the first and second-order inclusion probabilities associated with a BIRSS design. We show that the size of a BIRSS sample is random and propose using a conditional Poisson sampling (CPS) design to rectify this problem. We then use calculated inclusion probabilities to obtain design-based estimators of correlation coefficients between the bone mineral density (BMD) levels at the baseline and followup of a longitudinal BMD study in the province of Manitoba in Canada. We also study the problem of estimating the parameters of a regression model between the followup BMD and easy to obtain auxiliary information from the underlying population. Finally, we study the problem of classifying patients as those with or without osteoporosis using BIRSS and various CPS designs. We show that BIRSS designs are very flexible and can be used to obtain more efficient design-based estimators in sample surveys when dealing with response variables that are hard to measure or expensive to obtain.

Bayesian Estimation of Morgenstern Type Bivariate Rayleigh Distribution Using Some Types of Ranked Set Sampling

In this paper we consider Bayesian estimation based on bivariate ranked set sample, in which units are ranked based on measurements made on an easily and exactly measurable auxiliary variable X which is correlated with the study variable Y. We obtain Bayes estimator for the scale parameter of the study variate Y, when (X, Y ) follows a Morgenstern type bivariate Rayleigh distribution. The Bayes estimators are considered based on bivari-ate ranked set sampling, extreme ranked set sampling and maximum ranked set sampling with unequal sample. The accuracy of estimation methods in this paper is illustrated using simulation study. Finally, a real data set is analyzed.

Inference on $$P(X<Y)$$ for bivariate normal distribution based on ranked set sample

In this paper, we consider the problem of estimation of $$R=P(X<Y)$$, when X and Y are dependent, using bivariate ranked set sampling. The maximum likelihood estimates (MLEs) and Bayes estimates (BEs) of R are obtained based on ranked set sample when (X,Y) follows bivariate normal distribution. BEs are obtained based on both symmetric and asymmetric loss functions. The percentile bootstrap and HPD confidence intervals for R are also obtained. Simulation studies are carried out to find the accuracy of the proposed estimators. A real data is also used to illustrate the inferential procedures developed in this paper.

Estimating Morgenstern Type Bivariate Association Parameter Using a Modified Maximum Likelihood Method

This paper investigates estimating the association parameter of Morgenstern type bivariate distribution using a modified maximum likelihood method where the regular maximum likelihood methods failed to achieve estimation. The simple random sampling, concomitant of ordered statistics and bivariate ranked set sampling methods are used and compared. Efficiency and bias of the produced estimators are compared for two specific examples, Morgenstern type bivariate uniform and exponential distributions.

Estimating parameters of Morgenstern type bivariate distribution using bivariate ranked set sampling

This paper develops estimating parameters for Morgenstern type bivariatedistribution by using bivariate ranked set sampling procedure as an alterna-tive method to simple random sampling. This proposed procedure gives anopportunity to estimate all distribution's parameters simultaneously whichis not investigated in previous studies, yet. In the last part of this paper,simulation studies show properties of the new estimators and compare themwith some other existed estimators.

Other approaches to bivariate ranked set sampling

Other Approaches to Bivariate Ranked Set Sampling، للحصول على النص الكامل يرجى زيارة مكتبة الحسين بن طلال في جامعة اليرموك او زيارة موقعها الالكتروني

Estimation ofP(X&amp;gt;Y) whenXandYare dependent random variables using different bivariate sampling schemes

The stress-strength models have been intensively investigated in the literature in regards of estimating the reliability = P (X > Y) using parametric and nonparametric approaches under different sampling schemes when X and Y are independent random variables. In this paper, we consider the problem of estimating when (X; Y) are dependent random variables with a bivariate underlying distribution. The empirical and kernel estimates of = P (X > Y), based on bivariate ranked set sampling (BVRSS) are considered, when (X; Y) are paired dependent continuous random variables. The estimators obtained are compared to their counterpart, bivariate simple random sampling (BVSRS), via the bias and mean square error (MSE). We demonstrate that the suggested estimators based on BVRSS are more efficient than those based on BVSRS. A simulation study is conducted to gain insight into the performance of the proposed estimators. A real data example is provided to illustrate the process.

On stratified bivariate ranked set sampling with optimal allocation for naïve and ratio estimators

ABSTRACTThe purpose of the current work is to introduce stratified bivariate ranked set sampling (SBVRSS) and investigate its performance for estimating the population mean using both naïve and ratio methods. The properties of the proposed estimator are derived along with the optimal allocation with respect to stratification. We conduct a simulation study to demonstrate the relative efficiency of SBVRSS as compared to stratified bivariate simple random sampling (SBVSRS) for ratio estimation. Data that consist of weights and bilirubin levels in the blood of 120 babies are used to illustrate the procedure on a real data set. Based on our simulation, SBVRSS for ratio estimation is more efficient than using SBVSRS in all cases.

On stratified bivariate ranked set sampling for regression estimators

We investigate the relative performance of stratified bivariate ranked set sampling (SBVRSS), with respect to stratified simple random sampling (SSRS) for estimating the population mean with regression methods. The mean and variance of the proposed estimators are derived with the mean being shown to be unbiased. We perform a simulation study to compare the relative efficiency of SBVRSS to SSRS under various data-generating scenarios. We also compare the two sampling schemes on a real data set from trauma victims in a hospital setting. The results of our simulation study and the real data illustration indicate that using SBVRSS for regression estimation provides more efficiency than SSRS in most cases.

On regression analysis using modified bivariate ranked set sampling design (BVRSS)

Research on several forms of ranked set samples had been done by many researchers recently for estimating the population mean and other parameters. The results have ascertained that the ranked set samples are proven to be more efficient than the simple random samples in many situations. In this paper, modified bivariate ranked set sample (MBVRSS) was introduced to estimate a simple linear regression model when the regressors were assumed to be random. A primary data was collected on age and height in meter of 200 people from Ijebu-North Local Government Area of Ogun State. It is then shown that MBVRSS gives unbiased and highly efficient estimators of the regression model parameters, than those obtained by using bivariate simple random sampling (BVSRS), RSS or BVRSS using the same number of sample size. Key words: Modified bivariate ranked set sampling (MBVRSS), bivariate ranked-set sampling (BVRSS), bivariate simple random sampling (BVSRS) ranked set sampling (RSS), simple random sampling (SRS), simple linear regression.

An optimal sign test for one-sample bivariate location model using an alternative bivariate ranked-set sample

The aim of this paper is to find an optimal alternative bivariate ranked-set sample for one-sample location model bivariate sign test. Our numerical and theoretical results indicated that the optimal designs for the bivariate sign test are the alternative designs with quantifying order statistics with labels {((r+1)/2, (r+1)/2)}, when the set size r is odd and {(r/2+1, r/2), (r/2, r/2+1)} when the set size r is even. The asymptotic distribution and Pitman efficiencies of these designs are derived. A simulation study is conducted to investigate the power of the proposed optimal designs. Illustration using real data with the Bootstrap algorithm for P-value estimation is used.

On the optimality of bivariate ranked set sample design for the matched pairs sign test

An optimal alternative bivariate ranked set sample designs for the matched pairs sign test are obtained. Our investigation revealed that the optimal bivariate ranked set sample designs for matched pairs sign test are those with quantifying order statistics with labels {((r+1)/2, (r+1)/2)} when the set size r is odd and {(r/2, r/2), (r/2 + 1, r/2 + 1)} when the set size r is even. The exact null distributions, asymptotic distributions and Pitman efficiencies of those designs are derived. Numerical analysis of the power of the proposed optimal designs is included. An illustration using real data with a bootstrap algorithm for P-value estimation is used.

An Optimal Bivariate Ranked Set Sample Design for the Matched Pairs Sign Test

Abstract An optimal alternative bivariate ranked set sample designs for the matched pairs sign test are obtained. The exact null distributions, asymptotic distributions and Pitman efficiencies of those designs are derived. Numerical analysis of the power of the proposed optimal designs is included. Illustration using real data is used.

The matched pair sign test using bivariate ranked set sampling for different ranking based schemes

Bivariate rank set sample (BVRSS) matched pair sign test is introduced and investigated for different ranking based schemes. We show that this test is asymptotically more efficient and more powerful than its counterpart sign test based on a bivariate simple random sample (BVSRS) for different ranking schemes. The asymptotic null distribution and the efficiency of the test are derived. Pitman’s asymptotic relative efficiency is used to compare the asymptotic performance of the matched pair sign test using BVRSS versus using BVSRS in all ranking cases. For small sample sizes, the bootstrap method is used to estimate P -values. Numerical comparisons are used to gain insight about the efficiency of the BVRSS sign test compared to the BVSRS sign test. Our numerical and theoretical results indicate that using any ranking scheme of BVRSS for the matched pair sign test is more efficient than using BVSRS.

On the matched pairs sign test using bivariate ranked set sampling: an application to environmental issues

The matched pairs sign test using bivariate ranked set sampling (BVRSS) is introduced and investigated. We show that this test is asymptotically more efficient than its counterpart sign test based on a bivariate simple random sample (BVSRS). The asymptotic null distribution and the efficiency of the test are derived. The Pitman asymptotic relative efficiency is used to compare the asymptotic performance of the matched pairs sign test using BVRSS versus using BVSRS. For small sample sizes, the bootstrap method is used to estimate P-values. Numerical comparisons are used to gain insight about the efficiency of the BVRSS sign test compared to the BVSRS sign test. Our numerical and theoretical results indicate that using BVRSS for the matched pairs sign test is substantially more efficient than using BVSRS. Illustration using palm trees data from sultanate of Oman is provided. Key words: Bootstrap method, bivariate ranked set sample, power of the test, P-value of the test, Pitman’s relative efficiency, sign test

On Bivariate Ranked Set Sampling for Ratio and Regression Estimators

Relative performance of bivariate ranked set sampling (BVRSS), with respect to ranked set sampling (RSS) and simple random sampling (SRS), for estimating the population mean using ratio and regression methods is investigated. Properties of the proposed estimators are derived. Simulation study is conducted to gain insight in the behaviour of the relative efficiency of BVRSS relative to other sampling scheme. Also, real data that consist of heights and diameters of 399 trees are used to illustrate the procedure. The result of the simulation study and the real data illustration indicate that using BVRSS for ratio and regression estimation is more efficient than using a SRS and an RSS in most of the cases.

Bivariate Sign Test for One-Sample Bivariate Location Model Using Ranked Set Sample

In this article, we introduce a bivariate sign test for the one-sample bivariate location model using a bivariate ranked set sample (BVRSS). We show that the proposed test is asymptotically more efficient than its counterpart sign test based on a bivariate simple random sample (BVSRS). The asymptotic null distribution and the non centrality parameter are derived. The asymptotic distribution of the vector of sample median as an estimator of the locations of the bivariate model is introduced. Theoretical and numerical comparisons of the asymptotic efficiency of the BVRSS sign test with respect to the BVSRS sign test are also given.

Estimation of the Correlation Coefficient Using Bivariate Ranked Set Sampling with Application to the Bivariate Normal Distribution

Bivariate ranked set sampling BVRSS was introduced by Al-Saleh and Zheng (2002) as a bivariate version of the ordinary ranked set sampling (RSS). The procedure can be used when we deal with two characteristics simultaneously. In this article, the BVRSS procedure is used to estimate the correlation coefficient between two variables. The proposed estimators are compared to other existing estimators based on bivariate simple random sample BVSRS. The case of bivariate normal distribution is considered in details.

On Bivariate Ranked Set Sampling for Distribution and Quantile Estimation and Quantile Interval Estimation Using Ratio Estimator

As an extension to ranked set sampling (RSS), bivariate ranked set sampling (BVRSS) was introduced by Al-Saleh and Zheng [Al-Saleh, M. F., Zheng, G. (2002). Estimation of bivariate characteristics using ranked set sampling. Aust. New Zealand J. Statist. 44:221–232] for multiple characteristics estimation. In this paper, BVRSS is investigated for estimating the joint and the marginal distribution functions using direct method of estimation. The estimation of a population quantiles of two characteristics based BVRSS, for given values of probability (p) using direct method of estimation, is investigated. Also, quantiles and quantiles intervals estimation, based on BVRSS, using ratio estimator is presented. It turns out that all the suggested estimators in this paper are more efficient than the corresponding estimators obtained by using bivariate SRS and the ordinary RSS with concomitant variable. Finally, the proposed methods are illustrated using real data set of the trees.