Estimation of the critical transition probability using quadratic polynomial approximation with skewness-based reject option

Critical transitions and early warning signals are gaining attention in various fields such as ecology, climatology, and economics. However, quantitative estimation of the critical transition probability remains difficult. In this study, I propose a method to estimate the critical transition probability. It is based on a previous method using quadratic polynomial approximation, and skewness filtering is added as a reject option. The proposed method is applied to May model, a mathematical model of an ecosystem, as an example case. The results of numerical simulations show that the proposed method has much better precision than the previous method without skewness filtering, achieving a relative error of approximately +/- 50 % for the mean escape time.