New confidence interval estimator of the signal-to-noise ratio based on asymptotic sampling distribution

Abstract

In this paper, the asymptotic distribution of the signal-to-noise ratio (SNR) is derived and a new confidence interval for the SNR is introduced. An evaluation of the performance of the new interval compared to Sharma and Krishna (S–K) (1994) confidence interval for the SNR using Monte Carlo simulations is conducted. Data were randomly generated from normal, log-normal, χ2, Gamma, and Weibull distributions. Simulations revealed that the performance of S–K interval is totally dependent on the amount of noise introduced and that it has a constant width for a given sample size. The S–K interval performs poorly in four of the distributions unless the SNR is around one. It is recommended against using the S–K interval for data from log-normal distribution even with SNR = 1. Unlike the S–K interval which does not account for skewness and kurtosis of the distribution, the new confidence interval for the SNR outperforms S–K for all five distributions discussed, especially when SNR ⩾ 2. The proposed ranked set sampling (RSS) instead of simple random sampling (SRS) has improved the performance of both intervals as measured by coverage probability.