Bootstrap Confidence Intervals for Common Signal-to-noise Ratio of Two-parameter Exponential Distributions

Abstract

Signal-to-noise ratio (SNR) is a reciprocal of coefffficient of variation. The SNR is a measure of mean relative to the variability. Confidence procedures for common SNR of two-parameter exponential distributions were developed using generalized confidence interval (GCI) approach, large sample (LS) approach, adjusted method of variance estimates recovery (Adjusted MOVER) approach, and bootstrap approaches based on standard bootstrap (SB) and parametric bootstrap (PB). The performances of all approaches are measured by coverage probability and average length. Simulation studies show that all approaches have the coverage probabilities below the nominal confidence level of 0.95 when the common SNR is negative value. However, the coverage probabilities of all approaches are greater than the nominal confidence level of 0.95 when the common SNR is positive value. Moreover, the LS and AM approaches are the conservative confidence intervals. In addition, the GCI and PB approaches provide the confidence intervals with coverage probabilities close to the nominal confidence level of 0.95 when the sample sizes are large and the common SNR is positive value. The GCI and PB approaches are recommended to estimate the confidence intervals for the common SNR of two-parameter exponential distributions. Finally, all proposed approaches are employed in the data of the survival days of lung cancer patients for a demonstration.