Since it started observing the sky, the INTEGRAL satellite has discovered new categories of high mass X-ray binaries (HMXB) in our Galaxy. These observations raise important questions on the formation and evolution of these rare and short-lived objects. We present here new infrared observations from which to reveal or constrain the nature of 15 INTEGRAL sources, which allow us to update and discuss the Galactic HMXB population statistics. After previous photometric and spectroscopic observing campaigns in the optical and near-infrared, new photometry and spectroscopy was performed in the near-infrared with the SofI instrument on the ESO/NTT telescope in 2008 and 2010 on a sample of INTEGRAL sources. These observations, and specifically the detection of certain features in the spectra, allow the identification of these high-energy objects by comparison with published nIR spectral atlases of O and B stars. We present photometric data of nine sources (IGR J10101-5654, IGR J11187-5438, IGR J11435-6109, IGR J14331-6112, IGR J16328-4726, IGR J17200-3116, IGR J17354-3255, IGR J17404-3655, and IGR J17586-2129) and spectroscopic observations of 13 sources (IGR J10101-5654, IGR J11435-6109, IGR J13020-6359, IGR J14331-6112, IGR J14488-5942, IGR J16195-4945, IGR J16318-4848, IGR J16320-4751, IGR J16328-4726, IGR J16418-4532, IGR J17354-3255, IGR J17404-3655, and IGR J17586-2129). Our spectroscopic measurements indicate that: five of these objects are Oe/Be high-mass X-ray binaries (BeHMXB), six are supergiant high-mass X-ray binaries (sgHMXB), and two are sgB[e]. From a statistical point of view, we estimate the proportion of confirmed sgHMXB to be 42% and that of the confirmed BeHMXB to be 49%. The remaining 9% are peculiar HMXB.