  It has been long debated whether the high-energy gamma-ray radiation from the
Crab nebula stems from leptonic or hadronic processes. In this work, we
investigate the multi-band non-thermal radiation from the Crab pulsar wind
nebula with the leptonic and leptonic-hadronic hybrid models, respectively.
Then we use the Markov Chain Monte Carlo(MCMC) sampling technology and method
of sampling trace to study the stability and reasonability of the model
parameters according to the recent observed results and obtain the best-fitting
values of parameters. Finally, we calculate different radiative components
generated by the electrons and protons in the Crab nebula. The modeling results
indicate that the pure leptonic origin model with the one-zone only can partly
agree with some segments of the data from various experiments (including the
$\rm PeV$ gamma-ray emission reported by the LHAASO and the other radiation
ranging from the radio to very high energy (VHE) gamma-ray waveband), and the
contribution of hadronic interaction is hardly constrained. However, we find
that the hadronic process may also contribute, especially in the energy range
exceeding the $\rm PeV$. In addition, it can be inferred that the higher energy
signals from the Crab nebula could be observed in the future.
