This paper presents a comparative analysis of two approaches for estimating a Partition Markov Model, see García and González-López (Entropy, 19(4), 160 (2017)), to investigate the stochastic behavior of the Epstein-Barr virus (EBV) using its B95-8 genetic sequence (Baer, et al. Nature, 310, 207–211 (1984)). EBV has been associated with various cancers, including Burkitt’s lymphoma. The B95-8 sequence, extracted from a North American infectious mononucleosis case, serves as a sample of a stochastic process on the genetic alphabet \(\Lambda = \{\) a, c, g, t \(\}.\) The primary focus of the analysis is on estimating the Partition Markov Model using two comparative criteria. The selection of these two approaches is guided by the Efficient Determination Criterion (EDC) proposed by Zhao et al. (Statistical Inference for Stochastic Processes, 4(3), 273–282 (2001)). The findings contribute to our understanding of the stochastic behavior of EBV. The results of this study reveal an interesting finding, indicating that around 20% of the state space, constituted by concatenation of triples derived from \(\Lambda,\) consists of states that are classified equivalently by both estimation approaches. This observation suggests a significant overlap in the characterization of these states, regardless of the specific approach used for estimation. This finding has important implications for further research and advancing our understanding of EBV’s stochastic characteristics. The identified set of states, which are classified consistently by both approaches, may serve as potential correlates associated with the action of EBV. Exploring the properties and dynamics of these states can provide valuable insights into the behavior of the virus.