Simple Closed-Form Confidence Intervals for a Two-Parameter Exponential Distribution: One- and Two-Sample Problems

• Activity Number: 660
• Type: Contributed
• Date/Time: Thursday, August 13, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): Yanping Xia* and Kalimuthu Krishnamoorthy
• Companies: Southeast Missouri State University and University of Louisiana
• Keywords: Coverage Probability ; Generalize Pivotal Quantity ; Tolerance Limits ; MNA Approximation

Abstract

The problems of interval estimating the mean, quantiles and survival probability in a two-parameter exponential distribution are addressed. Modified normal-based approximations are used to find percentiles of appropriate pivotal quantities for estimating the mean and quantiles. Closed-form confidence intervals for survival probabilities are also given. Furthermore, a simple method of finding confidence intervals for the difference between two means and for the difference between two location parameters is proposed. Monte Carlo evaluation studies indicate that the approximate confidence intervals are accurate even for small samples. The methods are illustrated using two examples.