  We suggest the existence of systems in which the statistics of a particle
changes with the quantum level it occupies. The occupation numbers in thermal
equilibrium depend on a continuous statistical parameter that interpolates
between bosonic or fermionic and ghost-like statistical distributions. We call
such particle states ``ninions'': they are different from anyons and can exist
in 3+1 dimensions. We suggest that ninions can be associated with coherent
angular momentum states. In the Euclidean imaginary-time formalism, the
ninionic statistics can be implemented via the rotwisted boundary conditions,
which are associated with the rigid global rotation of the system with an
imaginary angular frequency. The imaginary rotation is characterized by a
PT-symmetric non-Hermitian Hamiltonian and possesses a well-defined
thermodynamic limit. The physics of ninions in thermal equilibrium is
accessible for numerical simulations on Euclidean lattices. We provide a no-go
theorem on the absence of analytical continuation between real and imaginary
rotations in the thermodynamic limit. The ground state of ninions shares
similarity with the $\theta$-vacuum in QCD. The ninions can produce negative
pressure and energy, similar to the Casimir effect and the cosmological dark
energy. In the thermodynamic limit, the dependence of thermal energy of free
ninions on the statistical parameter is a fractal.
