Ionospheric scintillation is a phenomenon that occurs after sunset, especially in the low-latitude region, affecting radio signals that propagate through the ionosphere. Depending on geophysical conditions, ionospheric scintillation may cause availability and precision problems to Global Navigation Satellite System users. The present work is concerned with the development of an extended model for describing the effects of the amplitude ionospheric scintillation on GPS receivers. Using the α-μ probabilistic model, introduced by previous authors in different contexts, the variance of GPS receiver tracking loop error may be estimated more realistically. The proposed model is developed with basis on the α-μ parameters and also considering correlation between amplitude and phase scintillation. Its results are interpreted to explain how a receiver may experience different error values under the influence of ionospheric conditions leading to a fixed scintillation level S4. The model is applied to a large experimental data set obtained at São José dos Campos, Brazil, near the peak of the equatorial anomaly during high solar flux conditions, between December 2001 and January 2002. The results from the proposed model show that depending on the α-μ pair, moderate scintillation (0.5 ≤ S4 ≤ 0.7) may be an issue for the receiver performance. When S4 > 0.7, the results indicate that the effects of scintillation are serious, leading to a reduction in the receiver availability for providing positioning solutions in approximately 50% of the cases.