  Impurities and defects are ubiquitous in topological insulators (TIs) and
thus understanding the effects of disorder on electronic transport is
important. We calculate the distribution of the random conductance fluctuations
$P(G)$ of disordered 2D TI wires modeled by the Bernevig-Hughes-Zhang (BHZ)
Hamiltonian with realistic parameters. As we show, the disorder drives the TIs
into different regimes: metal (M), quantum spin-Hall insulator (QSHI), and
ordinary insulator (OI). By varying the disorder strength and Fermi energy, we
calculate analytically and numerically $P(G)$ across the entire phase diagram.
The conductance fluctuations follow the statistics of the unitary universality
class $\beta=2$. At strong disorder and high energy, however, the size of the
fluctutations $\delta G$ reaches the universal value of the orthogonal symmetry
class ($\beta=1$). At the QSHI-M and QSHI-OI crossovers, the interplay between
edge and bulk states plays a key role in the statistical properties of the
conductance.
