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We investigate the nature of a class of probability density functions, sayG(a), with a the shape parameter, which generalizes the Gumbel distribution.These functions appear in a model of charge transport, when applied to ametal-insulator-metal structure, where the insulator is constituted by amonolayer of bacteriorhodopsin. Current shows a sharp increase above about 3 V,interpreted as the cross-over between direct and injection sequential-tunnelingregimes.  In particular, we show that, changing the bias value, the probability densityfunction changes its look from bimodal to unimodal. Actually, the bimodaldistributions can be resolved in at least a couple of $G(a)$ functions withdifferent values of the shape parameter.

Generalized Gumbel distribution of current fluctuations in purple membrane monolayers