Minimum Volume Confidence Sets for Two-Parameter Exponential Distributions

ABSTRACT

Under a reasonable restriction, we create the minimum volume confidence set for location and scale parameters of the exponential distribution. Compared to existing methods, none of which has a minimum-area property, the new confidence set is significantly the best (most accurate) with smallest volume, for whatever confidence level, sample size, and sample data.

KEYWORDS:

• Confidence level
• Critical value
• Pivotal quantity
• Restriction

Acknowledgments

The author thanks editors and anonymous referees for valuable comments and suggestions.

Additional information

Funding

This research is supported by the Natural Science Foundation of China (NSFC, Grant No. 11561073, 11461079).