Hansen's Method Applied to the Inversion of the Incomplete Gamma Function, with Applications

Analytical Approximation Algorithm for the Inverse of the Power of the Incomplete Gamma Function Based on Extreme Value Theory

“…It can be observed that with moderate values of n and α , the solutions obtained using the proposed algorithm fit the exact values obtained using the Newton iterative method more closely than those determined using the algorithms in [10] and [16]. In addition, the proposed algorithm and the algorithm in [16] are greatly affected by q .…”

“…To evaluate the algorithm, its performance was simulated and analyzed under different parameter settings, as described in this section, and it has been compared to the existing approximate analytical algorithms proposed in [10], [16] and the Newton iteration method [9].…”

“…The results show that the greater the q , the better the performance of the proposed algorithm. (2) Influence of α on the performance of the proposed algorithm In equation (10), when n =1000 and {0.9, 0.99, 0.999} q = , α varies from 4 to 40 with the step size 2. Fig.…”

“…Here, we describe the performance comparison of the proposed method with those of the methods in [10], [16], and the Newton iteration method [9]. The simulation platform was Dell (model: 131WL), and the processor was Intel (R) core (TM) i5-8265u (1.8 GHz).…”

“…However, an exact analytical solution method is yet to be devised for the problem of the inverse of the power of the incomplete Gamma function; thus, a common means of addressing such problems is to transform them into incomplete Gamma function inverse problems. The existing algorithms can be divided into two categories: algorithms based on numerical evaluation [8][9] and algorithms related to the analytical expression [10][11]. Although the algorithms based on numerical evaluation have higher accuracy, they inevitably have common shortcomings.…”