*Probability density function, *Monte Carlo method, *Solar energy, *Energy consumption, *Gaussian distribution, *Building-integrated photovoltaic systems

Energy hubs integrating onsite renewable generation and battery storage provide cost-efficient solutions for meeting building electricity requirements. This study presents methods for modeling uncertainties in load demand and solar generation, ranging from normal distribution assumptions to distributions sourced from CityLearn 2.3.0. We also implement kernel density estimation (KDE) to represent the non-parametric distribution characteristics of actual data. Through Monte Carlo simulation, we emphasize the value of robust, data-driven methodologies in optimizing energy hub operations under realistic uncertainty conditions and effectively conducting risk assessment. The CityLearn real-world data confirms that the non-Gaussian nature of building-level energy demand and solar PV electricity output is most accurately represented through KDE, leading to more precise cost projections for the considered energy hub. [ABSTRACT FROM AUTHOR]

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