The general procedure is as follows: 1. Suppose we are interested in whether a particular value (called the focal value) of a parameter of interest is "compatible" with the observed data.
For an integer k, letting ν2k -2π, γ) be the k-order focal value of the origin of system (2.7)δ = 0. Theorem 2.1.
(1) For any positive integer m, ν2m -2π) is called the m-th focal value of system (2.5) in the origin.
For any positive integer m, ν2m -2π) is called the m-order focal value of system (2.2) in the origin.
Evidently, if system (2.1) is a real system, v 2 k + 1 ( 2 π ) ( k = 1, 2, … ) is the k th focal value of the origin.
For any positive integer m, ν 2 m ( − 2 π ) is called the m th focal value of system (2.5) in the origin.
When all ε-order focal values are zero, we compute (varepsilon^{2} -order focal varepsilon^{2} -order).
According to the method in the article [11, 12], to compute the Liyapunov constants (or focal values) of the origin of system (2.8), we obtain the Lyapunov constants (or focal values) of the origin of (2.8) (namely the focal values of the equilibrium ( 1, 0 ) of model (1.2)) as follows.
Given a specified focal value for a target parameter (typically the null value, but possibly a non-null value like that representing a twofold risk), the difference between the focal value and the nearest boundary of the confidence interval for the parameter is calculated.
Here we are glad to highlight the work of Liu and Li [20], where a new definition of the focal value, quasi-Lyapunov constant, are given for the three-order nilpotent critical point.
