1. A display driver converting input display image data so that a part of a distribution of cumulative values of the number of pixels of each grayscale of the input display image data for one or plural frames is extended in a grayscale direction, and displaying the converted display image data on a display device, the display driver comprising: a conversion circuit which performs the conversion in accordance with a linear function when the grayscale of the display image data is a grayscale smaller than a specific grayscale and performs the conversion in accordance with a non-linear function including a ratio determined by a first difference between a maximum grayscale and a threshold grayscale and a second difference between the specific grayscale and the threshold grayscale when the grayscale of the display image data is equal to or higher than the specific grayscale, wherein a cumulative number of pixels of each grayscale between the threshold grayscale and the maximum grayscale is a predetermined proportion of the total number of pixels of the input display image data, wherein the specific grayscale is determined by multiplying the first difference between the maximum grayscale and the threshold grayscale by a constant value, wherein the conversion circuit performs the conversion to a grayscale corresponding to the cumulative value of the number of pixels of each grayscale equal to or higher than the specific grayscale of the display image data when the grayscale of the display image data is equal to or higher than the specific grayscale, a calculation circuit for measuring the number of pixels of each grayscale of the display image data and calculating the threshold grayscale, wherein the calculation circuit divides the display image data into a plurality of regions, measures the number of pixels of each grayscale of each region, and calculates a threshold grayscale of each region at which a cumulative value from the maximum grayscale reaches a predetermined proportion of the total number of pixels of each region, and a ratio of a difference between the specific grayscale and the threshold grayscale and a difference between the specific grayscale and a maximum grayscale that can be displayed on the display device is determined in accordance with a maximum value of the plurality of threshold grayscales of each region.