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This paper estimates the monthly, seasonal and yearly optimal tilt angles that maximize solar irradiation received on an inclined surface, thus enhancing the energy harvested. The uncertainties in global and diffuse radiations on the horizontal surface are accounted using stochastic analysis of their daily statistical measured data. The measured data is taken over a seven-year time span. The study is carried out for south-facing flat plate solar collectors at the Bangkok site, Thailand, situated in the northern hemisphere. The position of the sun at any time and location is predicted by the mathematical procedure of Julian dating. Further, four isotropic and anisotropic sky models are used to evaluate the ratio of diffuse solar radiation on an inclined surface to that on a horizontal surface. The best sky model is opted by using the ranking method of errors and is used for further analysis. Moreover, the frequency distributions of global and diffuse radiations are studied using four types of probability density functions (PDFs), viz., Weibull, lognormal, gamma and beta. Kolmogorov–Smirnov (K-S) test is used as a criterion to find the best fit among the aforementioned PDFs. The proposed optimization problem is solved using particle swarm optimization with time-varying acceleration coefficients (PSO-TVAC). The monthly tilt angles obtained are found to be varying with respect to the corresponding latitude angle, suggested by the thumb rule. The collected energy using this tilt angle over a period of one year is found to be 588MJ/m2$588 \,{\rm{MJ/}}{{\rm{m}}^2}$in excess to that harvested using the latitude angle.