This chapter presents a comprehensive exploration of statistical methods for the estimation and analysis of diagnostic signals in a variety of contexts, ranging from spectral analysis to parameter estimation and hypothesis testing. Beginning with numerical parameters of diagnostic signals, the discussion extends to spectral correlation analysis, focusing on the calculation of moments, the power spectral density, and the correlation function from signal samples. The utilization of the Goertzel algorithm for efficient spectral density estimation highlights the chapter's contribution to spectral analysis techniques. Further, the application of Pearson's system of curves for empirical data distribution approximation underscores the chapter’s innovative approach to statistical analysis. The extract also delves into stationarity testing methods (F-test, t-test, and Kolmogorov–Smirnov test) critical for diagnostic reliability and defect identification, illustrating the chapter's diagnostic focus. In addressing statistical hypothesis testing, the chapter introduces a method based on the maximum likelihood principle for distinguishing hypotheses about the parameters of a multidimensional Gaussian distribution, demonstrating the chapter's depth in statistical methodology. Lastly, it explores the use of the Neyman-Pearson criterion in planning diagnostic tests, offering a practical framework for hypothesis distinction regarding system states. This exploration underscores the chapter’s significant contribution to both the theoretical and practical aspects of diagnostic signal analysis, providing valuable insights and methods for researchers and practitioners in the field.