A true linear black-to-white gradient should produce a flat histogram: each tone value appears with about the same frequency, so the count for each bin is similar.

The key is that a histogram shows pixel value distribution, not human visual sensitivity. On the x-axis are tone values; on the y-axis is how many pixels have each value. If the gradient steps evenly from black to white, the histogram is flat regardless of how we perceive those tones.

Human brightness perception is roughly logarithmic, meaning we notice smaller changes more easily in darker tones than in brighter ones. That affects how a gradient looks to us, but not what its histogram should be if the stored pixel values are evenly spaced.

If your histogram rises at the ends, that is likely due to how the software generated or displayed the gradient or histogram—such as color space, gamma, smoothing, or bit-depth conversions. Some tools also apply a perceptual “smoothness” curve rather than a strictly linear ramp, which changes the histogram shape.