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We use data of $\sim$13,000 stars from the SDSS/APOGEE survey to study theshape of the bulge MDF within the region $|\ell|\leq11^\circ$ and$|b|\leq13^\circ$, and spatially constrained to ${\rm R_{GC}\leq3.5}$ kpc. Weapply Gaussian Mixture Modeling and Non-negative Matrix Factorizationdecomposition techniques to identify the optimal number and the properties ofMDF components. We find the shape and spatial variations of the MDF (at ${\rm[Fe/H]\geq-1}$ dex) are well represented as a smoothly varying contribution ofthree overlapping components located at [Fe/H]=+$0.32$, $-0.17$ and $-0.66$dex. The bimodal MDF found in previous studies is in agreement with ourtrimodal assessment once the limitations in sample size and individualmeasurement errors are taken into account. The shape of the MDF and itscorrelations with kinematics reveal different spatial distributions andkinematical structure for the three components co-existing in the bulge region.We confirm the consensus physical interpretation of metal-rich stars asassociated with the secularly evolved disk into a boxy/peanut X-shape bar. Onthe other hand, metal-intermediate stars could be the product of in-situformation at high redshift in a gas-rich environment characterized by violentand fast star formation. This interpretation would help to link a present-daystructure with those observed in formation in the center of high redshiftgalaxies. Finally, metal-poor stars may correspond to the metal-rich tail ofthe population sampled at lower metallicity from the study of RR Lyrae stars.Conversely, they could be associated with the metal-poor tail of the earlythick disc.

How Many Components? Quantifying the Complexity of the Metallicity Distribution in the Milky Way Bulge with APOGEE