Well testing is today a main procedure for verifying reservoir, well and fluid properties such as permeability, skin effect, average reservoir pressure, heterogeneities, boundaries and hydraulic connectivity. We present in this work a methodology based on numerical optimization and statistical methods to get an accurate and reliable Naturally Fractured Carbonate Vuggy Reservoir Characterization, using a Triple Porosity-Double Permeability Model. A sensitivity analysis is performed to identify the effect and magnitude on the pressure of each parameter involved in the model to reduce the error estimation and to eliminate multiple interpretations due to numerical precision. We also introduce a robust regularization method to control noise propagation contained in pressure data for improving well test analysis. The efficiency and accuracy of the proposed approach is demonstrated by implementing the triple porosity-double permeability model as compared with the traditional double-porosity model used in commercial software. Furthermore, not only the accuracy of the fit is compared but also the amount of reservoir information obtained when using the Triple Porosity-Double Permeability model, as we identify nine parameters in the case of totally penetrated wells and eleven parameters in the case of partially penetrated wells. Results are illustrated with transient well tests of real carbonate fractured vuggy reservoirs from Mexico.