## 1 Introduction
The SNR-based SF scheme focuses on SF assignment based on the target Signal-to-Noise Ratio (SNR) of the received packet and the impact of channel fading and distance [13]. The Best-Equal LoRa (BE-LoRa) algorithm was proposed to improve the packet delivery ratio (PDR) through the optimization and balancing of the SINR of received packets at the gateway for proper power setting and SF updates [14]. The RSSI-based and ToA-based schemes were designed to mitigate the co-SF interference during message transmission, thereby enhancing overall network efficiency and reliability. For instance, the EXPLoRa-SF algorithm compared the RSSI values with the sensitivity levels and divided them into six SF groups with equal numbers of nodes to create coexisting orthogonal sub-channels in the same channel bandwidth [15]. The authors also proposed the EXPLoRa-AT algorithm to balance the total offered packets (load) by utilizing the ordered waterfilling of SFs that then guaranteed the ToA equalization in each SF group. In [16], the authors proposed EXPLoRA-C, where the ordering of RSSI values and ToA-based techniques were combined using the concept of \"sequential waterfilling\" to assign the SF until the total offered packets in each SF group was full. The distance-based scheme involves assigning SFs to nodes based on their distances from the gateway. Examples include equal-interval-based (EIB) and equal-area-based (EAB) SF allocation methods [12]. In the EIB and EAB schemes, the network area was divided into concentric circles of equal intervals and equal areas, respectively. In the EIB scheme, lower SFs are assigned to nodes in inner annuli, which are closer to the gateway, resulting in higher packet success probability in interference-prone environments. Conversely, the EAB scheme improves packet success probability at longer distances by mitigating near-far effects in smaller outer annuli. In [17] and [18], the ML-based schemes were reported. In [17], the LR-RL method based on reinforcement learning (RL) for SF channel allocation in one-hop and in the LoRa mesh network was proposed. The method optimized the SF value based on channel traffic equilibrium by providing positive rewards for successful packet delivery and negative rewards otherwise. Consequently, the optimal SF value that minimizes SF collision rates was determined. In addition, [18] proposed a rapid, converging, decentralized RL algorithm for SF allocation aimed at maximizing packet reception ratio. Apart from the abovementioned schemes, the descriptive statistics approach has become another promising scheme to improve SF allocation due to its simplicity. In [19], the researchers proposed the Quantile Classification of Variance from the Mean (QCVM) method that uses the statistical method, namely, the quantile classification to group RSSI data considering their mean and probability density function (PDF). Then, they proposed the Standard Deviation (SD) classification method that analyzed RSSI data of nodes before separating them into groups by the standard deviation (SD) and re-assigning the SF values in each group [20]. Both descriptive statistics-based approaches were, however, constrained by the fixed number of SF subclasses allowed within each SF group. It is known that most SF allocation algorithm developments begin with simulations prior to the actual implementations. The node locations are commonly generated in the uniform random distribution, which is the default setting in most LoRaWAN simulators. However, the real-life node patterns often exhibit non-uniform or biased node distributions; thus, the uniform random distribution does not always give accurate insights in real-world scenarios [21, 22, 23] and potentially compromises the efficacy of prior algorithms in such contexts. This research introduces the Geometric Distribution (GD) algorithm, a novel inferential statistics approach that leverages the Probability Mass Function (PMF) of the geometric distribution mathematical model [24] to address the challenge of non-uniform or biased SF node distribution.