Extreme Trans-Neptunian Objects (ETNOs) are among the most distant objects in our solar system. These bodies have high perihelia (q > 40) and semi-major axes (a > 150) as well as highly elliptical orbits. This population has an abrupt perihelion cutoff at roughly 50 au. However, there are a few more-distant ETNOs, such as Sedna, that have much higher perihelia (q > 65); these objects are also referred to as Inner Oort Cloud objects (IOCs). This “gap” in perihelion between the ETNOs and the IOCs is poorly constrained and could provide insight into the structure of the outer solar system, including constraints for a hypothesized distant giant planet commonly referred to as Planet X or Planet 9. To determine the statistical significance of the perihelion gap we have developed a suite of observational survey simulations. In these simulations, synthetic objects in the gap and surrounding region are drawn from a variety of orbital element distributions. Each resulting synthetic object distribution is subjected to a variety of observational limits to determine detection rates. A Poissonian maximum likelihood is calculated for 10e4 simulation runs for each orbital element distribution. The results are then subjected to a set of statistical tests to determine agreement with the observed ETNO/IOC distribution. We then performed a Markov Chain Monte Carlo statistical fit on the observed distribution repeating the simulations and analyses for this population. These simulations indicate that the gap is a real feature of the outer solar system and not caused by observational bias. We also ran hundreds of dynamical simulations exploring the effect a distant giant planet would have on various hypothetical underlying ETNO/IOC distributions. These simulations contained the Sun, the four giant planets, a hypothetical Planet X, and hundreds to thousands of test particles drawn from various orbital element distributions similar to those used in the observational simulations. These systems were integrated for 4.5 Gyrs with a 0.2 year time step using the mercurius REBOUND integrator. The results of these simulations provide insight into the structure of the outer solar system and interactions between Planet X and the gap.