Confidence Intervals for Mean of Delta Two-Parameter Exponential Distribution

Abstract

AbstractThe two-parameter exponential distribution is widely used for many applications in real life, and the data can include zero observations. The mean, which represents the center of a population, is one of the parameters of interest. Herein, we propose confidence intervals for the mean of a delta two-parameter exponential distribution based on parametric bootstrapping (PB), standard bootstrapping (SB), the generalized confidence interval (GCI), and the method of variance estimates recovery (MOVER). The performances of the proposed confidence intervals were evaluated by using coverage probabilities and average lengths via Monte Carlo simulations. The results indicate that GCI can be recommended for small-to-moderate sample sizes whereas PB is appropriate for large sample sizes.KeywordsParametric bootstrapStandard bootstrapGeneralized confidence intervalMethod of variance estimates recoveryDelta two parameter exponential distribution