Performance of Statistical Methods for Testing the Signal-to-Noise Ratio of a Log-Normal Distribution

This study presents two statistical methods for testing the signal-to-noise ratio (SNR) of a log-normal distribution. The proposed statistical tests were based on the generalized confidence interval (GCI) approach and the large sample (LS) approach. To evaluate the performance of the proposed statistical tests, a simulation study was conducted under several values of SNR in a log-normal distribution. The performances of the statistical tests were compared based on the empirical size and power of the test. The simulation results showed that the statistical test based on the GCI approach performed better than the statistical test based on the LS approach in terms of the attained nominal significance level, and the empirical power of the test and is thus recommended for researchers. The performances of the proposed statistical tests also were examined through a numerical example.