In this paper, we propose an analytical model to estimate the signal-to-noise ratio (SNR) at the output of an adaptive equalizer in intensity modulation and direct detection (IMDD) optical transmission systems affected by shot noise, thermal noise, relative intensity noise (RIN), chromatic dispersion (CD) and bandwidth limitations. We develop the model as an extension of a previously presented one, and then we test its accuracy by sweeping the main parameters of a 4-PAM-based communication system such as RIN coefficient, extinction ratio, CD coefficient and equalizer memory. Our findings show a remarkable agreement between time-domain simulations and analytical results, with SNR discrepancies below 0.1 dB in most cases, for both feed-forward and decision-feedback equalization. We consider that the proposed model is a powerful tool for the numerical design of strongly band-limited IMDD systems using receiver equalization, as it happens in most of modern and future M-PAM solutions for short reach and access systems.