Aranked set sample (RSS), if not balanced, is simply a sample of independent order statistics generated from the same underlying distribution F. Kvam and Samaniego (1994) derived maximum likelihood estimates of F for a general RSS. In many applications, including some in the environmental sciences, prior information about F is available to supplement the data-based inference. In such cases, Bayes estimators should be considered for improved estimation. Bayes estimation (using the squared error loss function) of the unknown distribution function F is investigated with such samples. Additionally, the Bayes generalized maximum likelihood estimator (GMLE) is derived. An iterative scheme based on the EM Algorithm is used to produce the GMLE of F. For the case of squared error loss, simple solutions are uncommon, and a procedure to find the solution to the Bayes estimate using the Gibbs sampler is illustrated. The methods are illustrated with data from the Natural Environmental Research Council of Great Britain (1975), representing water discharge of floods on the Nidd River in Yorkshire, England
Copyright © 1999 Kluwer Academic Publishers.
The definitive version is available at: https://link.springer.com/article/10.1023/A%3A1009635315830
Kvam, Paul H., and Ram C. Tiwari. "Bayes Estimation of a Distribution Function Using Ranked Set Samples." Environmental and Ecological Statistics 6, no. 1 (1999): 11-22. https://doi.org/10.1023/A:1009635315830.
Kvam, Paul H. and Tiwari, Ram C., "Bayes Estimation of a Distribution Function Using Ranked Set Samples" (1999). Math and Computer Science Faculty Publications. 192.