Hyperstatistic S_p(X)

p = (5, 6) X = (H, W)

Cohort

M: 4082

F: 1986

Empirical

Theory

Simulation

M: 4082

F: 1986

$S_5\left(H\right)=\langle {\left(H-{\mu }_H\right)}^5\rangle /{\sigma }_H^5$

Mean $S_5\left(H\right)$

male

0.9679

1.1784

0.5997

1.0966

1.1013

female

0.4836

1.1907

0.6304

1.2628

0.5685

Standard Error $S_5\left(H\right)$

male

0.3983

0.4518

0.5016 | 0.1664

female

0.4835

0.6487

0.6943 | 0.2218

$S_5\left(W\right)=\langle {\left(W-{\mu }_W\right)}^5\rangle /{\sigma }_W^5$

Mean $S_5\left(W\right)$

male

4.8791

5.6489

7.6398

4.7215

5.6557

female

6.5463

5.4361

4.1332

3.7024

5.9618

Standard Error $S_5\left(W\right)$

male

0.5518

1.0841

2.9183 | 0.8604

female

1.3757

1.4869

2.2594 | 0.6926

$S_6\left(H\right)=\langle {\left(H-{\mu }_H\right)}^6\rangle /{\sigma }_H^6$

Mean $S_H^{\left(6\right)}$

male

15.6714

15.5060

15.9807

13.5489

14.4296

female

14.3941

15.5165

13.1332

15.0664

13.1147

Standard Error $S_H^{\left(6\right)}$

male

1.0394

1.4580

2.8475 | 0.7108

female

1.1307

2.0974

1.9517 | 0.6475

$S_6\left(W\right)=\langle {\left(W-{\mu }_W\right)}^6\rangle /{\sigma }_W^6$

Mean $S_6\left(W\right)$

male

21.3981

25.4523

38.8263

21.0697

26.7901

female

29.0534

24.7436

18.5144

17.0547

24.5282

Standard Error $S_6\left(W\right)$

male

1.9545

6.0795

17.7566 | 5.2329

female

6.0559

8.1822

7.4735 | 2.2870