We conduct a first comprehensive study of the Luminosity Function (LF) using a non-parametric approach. We use Gaussian Process to fit available luminosity data between redshifts z ∼ 2-8. Our free-form LF in the non-parametric approach rules out the conventional Schechter function model to describe the abundance-magnitude relation at redshifts z=3 and 4. Hints of deviation from the Schechter function are also noticed at redshifts 2, 7 and 8 at lower statistical significance. Significant deviation starts for brighter ionizing sources at M UV ≲ -21. The UV luminosity density data at different redshifts are then derived by integrating the LFs obtained from both methods with a truncation magnitude of -17. In our analysis, we also include the first 90 arcmin2 JWST/NIRCam data at z ∼ 9-12. Since at larger magnitudes, we do not find major deviations from the Schechter function, the integrated luminosity density differs marginally between the two methods. Finally, we obtain the history of reionization from a joint analysis of UV luminosity density data along with the ionization fraction data and Planck observation of Cosmic Microwave Background. The history of reionization is not affected by the deviation of LFs from Schechter function at lower magnitudes. We derive reionization optical depth to be τ re = 0.0494+0.0007 -0.0006 and the duration between 10% and 90% completion of ionization process is found to be Δ z ∼ 1.627+0.059 -0.071.