Measurements of quantum gravity could be made by looking at some of the proposed quantum gravity effects, such as fluctuations of space-time. The Lorentz invariance violation (LIV) effect appears as a consequence of the modified photon dispersion relation, used to model the effect of space-time fluctuations on gamma rays. Using the LIV time of flight analysis, we are able to look for quantum gravity effects using observations at energies much lower than the Planck scale. One of the most popular methods for the LIV time of flight analysis is the maximum likelihood method. In this thesis, we focused on looking at how the choice of the function used to create the light curve template affects the maximum likelihood analysis. The functions used were: i) sum of Gaussian distributions, ii) sum of Cauchy distributions, iii) sum of skewed Gaussian distributions, iv) Fourier series, v) Kernel density estimation. This analysis was based on simulations of observations of Markarian 421 on the night of 24 to 25 of April 2014, preformed by Major Atmospheric Gamma Imaging Cherenkov (MAGIC) telescopes. Fourier series and Kernel density estimation were not able to achieve a satisfying fit of the observed data, so their light curves were not used for the final maximum likelihood analysis. For the other functions, the fits managed to capture the structure of the light curve with more accuracy. Furthermore, their χ2 tests were very similar, so they made good candidates for comparison. The recreated light curves were then used in the LIVelihood software for LIV time of flight studies. Using simulations, LIV parameter λ was calculated along with the respective upper and lower limits to form a 95% confidence interval. The light curve template created using the sum of skewed Gaussian distributions was not converging in enough simulations for the λ distribution to be calculated. For the light curve templates created using the sum of Gaussian distributions and the sum of Cauchy distributions λ was calculated to be (−139.9±875) s/TeV and (−76.22±971) s/TeV, respectively. In addition, the lower limit on the energy at which the effects of quantum gravity become significant in the linear term were calculated from λ and amount to E(G) QG1 = 2.48557·10^17 GeV and E(C) QG1 = 3.11314·10^17 GeV for the sum of Gaussian distributions and the sum of Cauchy distributions light curve templates, respectively.