The index for evaluating the ability of color reproduction is required. The color distribution index (CDI) was proposed to comment the display ability of color distribution of reproduction in CIE Lu'v' color space. A cell of Just Noticeable Difference (JND) for luminance and chromaticity (u'v') was proposed to qualify whether the reproduced colors are in some region of color volume of display. Human eye can perceive fewer colors at low luminance, however, the scalar of chromaticity (u'v') JND at low luminance was the same with the one at other luminance. CDI will be distorted at low luminance. In this paper, regarding perceptible vision at low luminance, we try to use chromaticity (a*b*) JND to replace chromaticity (u'v') JND. The color distribution will be discussed in CIE La*b* color space. We find that CDI at low luminance in CIE L*a*b* color space is higher than in CIE Lu'v' color space, as well as different gamma curves and different bit depths affect CDI. The displays are going to keep approaching 100% true color reproduction; hence the index for evaluating the ability of color reproduction is required.