Confidence intervals for a two-parameter exponential distribution: One- and two-sample problems

ABSTRACT

The problems of interval estimating the mean, quantiles, and survival probability in a two-parameter exponential distribution are addressed. Distribution function of a pivotal quantity whose percentiles can be used to construct confidence limits for the mean and quantiles is derived. A simple approximate method of finding confidence intervals for the difference between two means and for the difference between two location parameters is also proposed. Monte Carlo evaluation studies indicate that the approximate confidence intervals are accurate even for small samples. The methods are illustrated using two examples.

KEYWORDS:

• Coverage probability
• Generalized pivotal quantity
• MNA approximation
• Tolerance limits

Acknowledgments

The authors are grateful to two reviewers for providing useful comments and suggestions. A suggestion by a reviewer lead to the exact calculation of the cdf of f_{n, c}.