High Dynamic Range (HDR) image provides higher perceptual quality such that it appears considerably more realistic and attractive for the human observer. Since most of current screens are Low Dynamic Range (LDR) screens, lots of researches have been proposed to design tone mapping algorithms converting the HDR images into a range that is suitable to display these tone mapped images on standard LDR screens. For this purpose, this paper first investigates the pixels distribution in the HDR image through the study of various traditional Histogram Equalization (HE) algorithms which were originally developed to improve the visual quality of LDR images such as the contrast enhancement of the latter. Moreover , a modification of the Histogram Adjustment based Linear to Equalized Quantizer (HALEQ), developed for HDR images, is proposed. Simulation results show that the proposed modification preserves more details than the original version of the algorithm in most parts of the HDR image.