In this thesis, I will present my research work with statistical analysis towards a galaxy’smorphology and its morphometric. The first part would be with the galaxy morphometric and have heavy focus with one particular software: Source Extractor. Source Extractor was compared to GALFIT in order to see how accurate and precise we would expect the software to be with effective radii, scale length, inclination,position angle, and major and minor axes. This is towards preparation for future surveys with expectation of a large boom in galaxy discovery with the new observatories to be online (EUCLID, LSST, JWST, etc.). From our understanding, Source Extractor is neither accurate nor precise enough to consider its initial computed parameters to be true. However, it does hold to see if there any sort of correlation or trend within the population. On the second part, we do scale-invariant morphological calculations on some galaxies that are high-redshift and ultra-luminous. We do computed statistical analytics to find and be certain of the morphological parameters. We only useGini value and asymmetry and on 10 z~8 galaxies with IRAC color. However, we do see more possible correlation with Gini and asymmetry in such epoch, yet very uncertain. However, just with these characteristics, this sample has an unusual pattern from what was expected, and this has an implication that morphological parameters may be useful for further surveys for candidacy testing, in that they can help identify the z~ 8 redshift galaxies with this unique characteristic. However, we need a larger sample size to be more certain, which is difficult to do as it is difficult to detect and discerna high-redshift galaxy. To create more certainty, we tested Gini and asymmetry on the star-forming, z~8 galaxies in the JAGUAR mock catalog. This shows that groupings do exist and shows the observed galaxies being more diffuse than expected by models. Correlations, however, still seem to be nonexistent. This shows using Gini and asymmetry in JWST surveys to test high-redshift candidates.