A new and generalized statistical model, called Málaga distribution (M distribution), has been derived recently to characterize the irradiance fluctuations of an unbounded optical wave front propagating through a turbulent medium under all irradiance fluctuation conditions. As great advantages associated to that model, we can indicate that it is written in a simple tractable closed-form expression and that it is able to unify most of the proposed statistical models for free-space optical communications derived until now in the scientific literature. Based on that Málaga model, we have analyzed in this paper the role of the detection threshold in a free-space optical system employing an on-off keying modulation technique and involved in different scenarios, and taking into account the extinction ratio associated to the employed laser. First we have derived some analytical expressions for the lower-bound performance of the free-space optical system with the light intensity fading induced by turbulence obtained when the additive white Gaussian noise is not present in the system. Then, we have analyzed the optimal threshold in the system and how it changes when atmospheric conditions vary. Finally, a closed form expression for the bit error rate of that system is derived.