A Characterization of Power Method Transformations through L-Moments

Figure 3

Third- and fifth-order standard normal-based polynomial approximations (dashed lines) of a Beta (𝛼=5, 𝛽=4) distribution. The L-moment ratios for this Beta distribution are given in Table 3. The fifth-order polynomial coefficients are 𝑐₁=.02697, 𝑐₂=1.071, 𝑐₃=−.0297, 𝑐₄=−.0312, 𝑐₅=.0009, and 𝑐₆=.00065. The third-order polynomial coefficients are 𝑐₁=.02576, 𝑐₂=0.9993, 𝑐₃=−.02576, and 𝑐₄=.00027.

(a)

(b)