Table of Contents
ISRN Probability and Statistics
Volume 2013, Article ID 237940, 7 pages
http://dx.doi.org/10.1155/2013/237940
Research Article

Minimum Variance Unbiased Estimation in the Gompertz Distribution under Progressive Type II Censored Data with Binomial Removals

Department of Statistics, Sardar Patel University, Vallabh Vidyanagar 388120, India

Received 30 October 2012; Accepted 19 November 2012

Academic Editors: B. L. Granovsky and X. Lu

Copyright © 2013 Ashok Shanubhogue and N. R. Jain. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper deals with the problem of uniformly minimum variance unbiased estimation for the parameter of the Gompertz distribution based on progressively Type II censored data with binomial removals. We have obtained the uniformly minimum variance unbiased estimator (UMVUE) for powers of the shape parameter and its functions. The UMVUE of the variance of these estimators is also given. The UMVUE of (i) pdf, (ii) cdf, (iii) reliability function, and (iv) hazard function of the Gompertz distribution is derived. Further, an exact % confidence interval for the th quantile is obtained. The UMVUE of pdf is utilized to obtain the UMVUE of . An illustrative numerical example is presented.