  We study the characterization and realization of higher-order topological
Anderson insulator (HOTAI) in non-Hermitian systems, where the non-Hermitian
mechanism ensures extra symmetries as well as gain and loss disorder.We
illuminate that the quadrupole moment $Q_{xy}$ can be used as the real space
topological invariant of non-Hermitian higher-order topological insulator
(HOTI). Based on the biorthogonal bases and non-Hermitian symmetries, we prove
that $Q_{xy}$ can be quantized to $0$ or $0.5$. Considering the disorder
effect, we find the disorder-induced phase transition from normal insulator to
non-Hermitian HOTAI. Furthermore, we elucidate that the real space topological
invariant $Q_{xy}$ is also applicable for systems with the non-Hermitian skin
effect. Our work enlightens the study of the combination of disorder and
non-Hermitian HOTI.
