Bounded risk per unit cost index constraint for sequential estimation of the mean in a two-parameter exponential distribution

Abstract

In this article, the two-stage sequential sampling procedure is proposed to estimate the mean of an exponential distribution under the modified square error loss function. The main aim of the article is to consider the associated risk per unit cost function by bounding it from above with a fixed preassigned positive number, ω. We provide the exact distribution of the total sample size, explicit formulas for the mathematical expectation of the rth power of the total sample size, the expected value and mean squared error of the maximum likelihood estimate of the scale, and mean parameters of the exponential distribution under the two-stage sequential procedure. The performances of the proposed methodologies are investigated with the help of simulations. In the end, we supplement with extensive sets of data analysis via computer simulations, validating that the two-stage sequential method performs very well. Finally, using a real data set, the procedure is clearly illustrated.

KEYWORDS:

• Bounded risk per unit cost
• cancer data
• first-order property
• location and scale parameters
• stopping rule
• two-stage sequential sampling

SUBJECT CLASSIFICATIONS:

• 62L15
• 60G40
• 62F12
• 60K10

ACKNOWLEDGEMENT

We thank and express our deep gratitude to the Editor-in-Chief Professor Nitis Mukhopadhyay, the Associate Editor, and the referees for their useful suggestions and comments, which helped us to improve the article. The authors also thank Yazd University for support this work.

DISCLOSURE

The authors have no conflicts of interest to report.