This paper investigates unmanned aerial vehicle (UAV)-mounted intelligent reflecting surfaces (IRS) to leverage the benefits of this technology for future communication networks, such as 6G. Key advantages include enhanced spectral and energy efficiency, expanded network coverage, and flexible deployment. One of the main challenges in employing UAV-mounted IRS (UMI) technology is the random fluctuations of hovering UAVs. Focusing on this challenge, this paper explores the capabilities of UMI with passive/active elements affected by UAV fluctuations in both horizontal and vertical angles, considering the three-dimensional (3D) radiation pattern of the IRS. The relationship between UAV fluctuations and IRS pattern is investigated by taking into account the random angular vibrations of UAVs. A tractable and closed-form distribution function for the IRS pattern is derived, using linear approximation and by dividing it into several sectors. In addition, closed-form expressions for outage probability (OP) are obtained using central limit theorem (CLT) and Gamma approximation. The theoretical expressions are validated through Monte Carlo simulations. The findings indicate that the random fluctuations of hovering UAVs have a notable impact on the performance of UMI systems. To avoid link interruptions due to UAV instability, IRS should utilize fewer elements, even though this leads to a decrease in directivity. As a result, unlike terrestrial IRS, incorporating more elements into aerial IRS systems does not necessarily improve performance due to the fluctuations in UAV. Numerical results show that the OP can be minimized by selecting the optimal number of IRS elements and using active elements.