Gumbel’s bivariate exponential distribution: estimation of the association parameter using ranked set sampling

2021 ◽  
Author(s):  
Yusuf Can Sevil ◽  
Tugba Ozkal Yildiz
Keyword(s):  
Exponential Distribution ◽  
Ranked Set Sampling ◽  
Bivariate Exponential Distribution ◽  
Distribution Estimation ◽  
Bivariate Exponential

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.

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.

BLOCK AND BASU'S BIVARIATE EXPONENTIAL DISTRIBUTION WITH APPLICATION TO DROUGHT DATA

2006 ◽  
Vol 21 (1) ◽  
pp. 143-155 ◽  
Author(s):  
Saralees Nadarajah ◽  
Samuel Kotz
Keyword(s):  
Exponential Distribution ◽  
Bivariate Exponential Distribution ◽  
Bivariate Exponential ◽  
Exact Distributions ◽  
Hydrological Applications

Motivated by hydrological applications, the exact distributions ofR=X+Y,P=XY, andW=X/(X+Y) and the corresponding moment properties are derived whenXandYfollow Block and Basu's bivariate exponential distribution. An application of the results is provided to drought data from Nebraska.

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