  Determining the statistics of elementary excitations supported by fractional
quantum Hall states is crucial to understanding their properties and potential
applications. In this paper, we use the topological entanglement entropy as an
indicator of Abelian statistics to investigate the single-component $\nu=2/5$
and $3/7$ states for the Hofstadter model in the band mixing regime. We perform
many-body simulations using the infinite cylinder density matrix
renormalization group and present an efficient algorithm to construct the area
law of entanglement, which accounts for both numerical and statistical errors.
Using this algorithm, we show that the $\nu=2/5$ and $3/7$ states exhibit
Abelian topological order in the case of two-body nearest-neighbor
interactions. Moreover, we discuss the sensitivity of the proposed method and
fractional quantum Hall states with respect to interaction range and strength.
