scholarly journals Inference on Downton’s Bivariate Exponential Distribution Based on Moving Extreme Ranked Set Sampling

2016 ◽  
Vol 42 (3) ◽  
pp. 161-179 ◽  
Author(s):  
Ahmed Ali Hanandeh ◽  
Mohammad Fraiwan Al-Saleh
Keyword(s):  
Exponential Distribution ◽  
Random Sampling ◽  
Simple Random Sampling ◽  
Ranked Set Sampling ◽  
Bivariate Exponential Distribution ◽  
Linear Combinations ◽  
Unbiased Estimators ◽  
Concomitant Variable ◽  
Bivariate Exponential ◽  
Extreme Ranked Set Sampling

The purpose of this paper is to estimate the parameters of Downton’sbivariate exponential distribution using moving extreme ranked set sampling(MERSS). The estimators obtained are compared via their biases andmean square errors to their counterparts using simple random sampling (SRS).Monte Carlo simulations are used whenever analytical comparisons are difficult.It is shown that these estimators based on MERSS with a concomitantvariable are more efficient than the corresponding ones using SRS. Also,MERSS with a concomitant variable is easier to use in practice than RSS witha concomitant variable. Furthermore, the best unbiased estimators among allunbiased linear combinations of the MERSS elements are derived for someparameters.

scholarly journals On Regression Estimators Using Extreme Ranked Set Samples

2004 ◽  
Vol 9 ◽  
pp. 67
Author(s):  
Hani M. Samawi ◽  
Ahmed Y.A. Al-Samarraie ◽  
Obaid M. Al-Saidy
Keyword(s):  
Random Sampling ◽  
Sampling Method ◽  
Simple Random Sampling ◽  
Auxiliary Variable ◽  
Ranked Set Sampling ◽  
Population Mean ◽  
Concomitant Variable ◽  
Regression Estimators ◽  
Monte Carlo Evaluation ◽  
Extreme Ranked Set Sampling

Regression is used to estimate the population mean of the response variable, , in the two cases where the population mean of the concomitant (auxiliary) variable, , is known and where it is unknown. In the latter case, a double sampling method is used to estimate the population mean of the concomitant variable. We invesitagate the performance of the two methods using extreme ranked set sampling (ERSS), as discussed by Samawi et al. (1996). Theoretical and Monte Carlo evaluation results as well as an illustration using actual data are presented. The results show that if the underlying joint distribution of and  is symmetric, then using ERSS to obtain regression estimates is more efficient than using ranked set sampling (RSS) or  simple random sampling (SRS).  

scholarly journals Generalized Exponential Distribution - Estimation of parameters using modifications in methods of Ranked Set Sampling

2021 ◽  
Author(s):  
Vyomesh Prahlad Nandurbarkar ◽  
Ashok Shanubhogue
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Exponential Distribution ◽  
Random Sampling ◽  
Simple Random Sampling ◽  
Ranked Set Sampling ◽  
Likelihood Method ◽  
Generalized Exponential Distribution ◽  
Data Set ◽  
Extreme Ranked Set Sampling

Abstract In this study, we estimate the parameters of the Generalized Exponential Distribution using Moving Extreme Ranked Set Sampling (MERSS). Using the maximum likelihood estimation method, we derive the expressions. MERSS estimates are compared with estimates obtained by simple random sampling (SRS) using a real data set. We also study the other variations of the methods of Ranked Set Sampling like Quartile Ranked Set Sampling(QRSS), Median Ranked Set Sampling(MRSS) and Flexible Ranked Set Sampling(FLERSS) (a scheme based on QRSS and MRSS). For known shape parameter values, we present coefficients for linear combinations of order statistics for least squares estimates. Here, the expressions are derived through maximum likelihood, and the estimates are calculated numerically. Simulated results indicate that estimates generated using least-squares and the maximum likelihood method for Ranked Set Sampling (RSS) perform better than those generated using Simple Random Sampling (SRS). Asymptotically, MERSS outperforms SRS, QRSS, MRSS, and FLERSS.

An Improved Estimation of Parameter of Morgenstern-Type Bivariate Exponential Distribution Using Ranked Set Sampling

2022 ◽  
pp. 1-25
Author(s):  
Vishal Mehta
Keyword(s):  
Exponential Distribution ◽  
Mean Squared Error ◽  
Ranked Set Sampling ◽  
Error Estimator ◽  
Bivariate Exponential Distribution ◽  
Ranked Set Sample ◽  
Minimum Mean Squared Error ◽  
Squared Error ◽  
Bivariate Exponential ◽  
Special Cases

In this chapter, the authors suggest some improved versions of estimators of Morgenstern type bivariate exponential distribution (MTBED) based on the observations made on the units of ranked set sampling (RSS) regarding the study variable Y, which is correlated with the auxiliary variable X, where (X,Y) follows a MTBED. In this chapter, they firstly suggested minimum mean squared error estimator for estimation of 𝜃2 based on censored ranked set sample and their special case; further, they have suggested minimum mean squared error estimator for best linear unbiased estimator of 𝜃2 based on censored ranked set sample and their special cases; they also suggested minimum mean squared error estimator for estimation of 𝜃2 based on unbalanced multistage ranked set sampling and their special cases. Efficiency comparisons are also made in this work.

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