Characterizing Tukey ℎ and ℎℎ-Distributions through 𝐿-Moments and the 𝐿-Correlation

Figure 1

Graph of an ℎℎ-distribution based on matching the conventional moments of a noncentral Student 𝑡_{(df=5,𝛿=1)} distribution. The values of ℎ_ℒ and ℎ_ℛ were determined by solving equations (A.3) and (A.4) in the appendix. The estimates (𝛼_3,4; 𝜏̂_3,4) and bootstrap confidence intervals (C.I.s) were based on resampling 25,000 statistics. Each sample statistic was based on a sample size of 𝑛=250.