This paper presents an extension of the integrated time-chirp rate analysis technique, known as the parameterized centroid frequency-chirp rate distribution (PCFCRD), for noisy multicomponent linear frequency modulated signals analysis. The PCFCRD is based on a newly defined correlation function and its auto term accumulation is two-dimensionally coherent. The principle, cross term characteristic, implementation, properties, parameter selection criterion, antinoise performance, and estimation accuracy are analyzed for the PCFCRD. In this paper, comparisons with the coherently integrated cubic phase function, maximum likelihood method, and Lv's distribution are performed. With mathematic analyses and numerical simulations, we demonstrate that the PCFCRD outperforms these three representative counterparts. Further, by combining with analyses of the PCFCRD, several unclear mechanisms of the constant delay introduction are mathematically interpreted, especially quantitative influences on the chirp rate resolution and theoretical antinoise performance.