  We consider a disordered one-dimensional tight-binding model with power-law
decaying hopping amplitudes to disclose wavefunction maximum distributions
related to the Anderson localization phenomenon. Deeply in the regime of
extended states, the wavefunction intensities follow the Porter-Thomas
distribution while their maxima assume the Gumbel distribution. At the critical
point, distinct scaling laws govern the regimes of small and large wavefunction
intensities with a multifractal singularity spectrum. The distribution of
maxima deviates from the usual Gumbel form and some characteristic finite-size
scaling exponents are reported. Well within the localization regime, the
wavefunction intensity distribution is shown to develop a sequence of
pre-power-law, power-law, exponential and anomalous localized regimes. Their
values are strongly correlated, which significantly affects the emerging
extreme values distribution.
