Global Lightning and Sprite Measurements on Japanese Experiment Module (JEM-GLIMS) started the nadir observations of lightning discharges and transient luminous events (TLEs) from the International Space Station (ISS) since November 2012. In the nadir observations, JEM-GLIMS optical instruments have to simultaneously detect incomparably intense lightning emissions and weak TLE emissions. To distinguish TLEs, especially sprite events, from lightning events, combined data analytical methods are adopted: (1) a subtraction of the wideband camera image from the narrowband camera image, (2) a calculation of the intensity ratio between different photometer channels, and (3) an estimation of the polarization and charge moment changes for the TLE-producing lightning discharges. We succeeded in identifying numbers of sprite events using the combined analytical methods, and here we report three sprite events detected by JEM-GLIMS as a case study. In the subtracted images, sprite emissions are located over the area of the sprite-producing lightning emissions. However, these sprites and sprite-producing lightning discharges did not occur at the nadir point of the ISS. For this reason, the geometry conversion of the sprite and sprite-producing lightning emissions as observed from the point just over the sprite-producing lightning discharges is performed. In the geometry-converted images, the locations of the sprite emissions are clearly displaced by 8-20 km from the peak positions of the sprite-producing lightning emissions. Thus, the first quantitative spatial distributions of sprites and sprite-producing lightning discharges from the JEM-GLIMS nadir observations are revealed.