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# International Journal of Statistics and Applied Mathematics

#### 2020, Vol. 5, Issue 3, Part A

##### Confidence intervals for difference of signal-to-noise ratios of two-parameter exponential distributions

Author(s): Warisa Thangjai and Sa-Aat Niwitpong

Abstract: Coefficient of variation is the standard deviation divided by the mean. It is a measure of relative variability in different units. Signal-to-noise ratio (SNR) is the reciprocal of coefficient of variation. It is the ratio of mean to standard deviation of measurement. The SNR is extensively used in many application fields. Exponential distribution describes the lengths of the inter-arrival times in a homogeneous Poisson process. For positively skewed data, the exponential distribution is as important as the normal distribution in sampling theory and statistics. Two-parameter exponential distribution has an important role in medical sciences and life testing. For two populations, the difference of SNRs of two-parameter exponential distributions is interesting. In this paper, the problem of constructing confidence intervals for difference of SNRs of two-parameter exponential distributions is considered. Generalized confidence interval (GCI) approach, large sample approach, method of variance estimates recovery (MOVER) approach, and parametric bootstrap (PB) approach are applied to construct the confidence intervals. Based on the simulation study, the results indicated that the coverage probability of the GCI approach does not depend on difference of SNRs, but the coverage probability is around the nominal confidence level of 0.95. The large sample and MOVER approaches provide the conservative confidence intervals when the value of 0 is large. The PB approach provides better in term of coverage probability. As a result, the PB approach is recommended to construct the confidence intervals for the difference of SNRs. The proposed approaches are illustrated using a real data set from medical science.  