Paraphrase the following text using more academic and scientific language Use a neutral tone and avoid repetitions of words and phrases：The survival probility $A_n$ of white red and blue noise with di

The present study investigates the survival probability, denoted as $A_n$, of white, red, and blue noise at various levels of noise intensity. Given the similarity between the autocorrelation functions of red noise and pink noise, as well as blue noise and purple noise, the latter two noises are not considered in the analysis. Notably, the amplitude probability of red noise surpasses that of white and blue noise, attributable to the atypical autocorrelation characteristic of red noise relative to the other two types of noise.