ダゴスティーノのK二乗検定
{\displaystyle {\begin{aligned}&\mu _{1}(g_{1})=0,\\&\mu _{2}(g_{1})={\frac {6(n-2)}{(n+1)(n+3)}},\\&\gamma _{1}(g_{1})\equiv {\frac {\mu _{3}(g_{1})}{\mu _{2}(g_{1})^{3/2}}}=0,\\&\gamma _{2}(g_{1})\equiv {\frac {\mu _{4}(g_{1})}{\mu _{2}(g_{1})^{2}}}-3={\frac {36(n-7)(n^{2}+2n-5)}{(n-2)(n+5)(n+7)(n+9)}}.\end{aligned}}}
標本尖度g2の分布の平均μ1(g2)、分散μ2(g2)、歪度γ1(g2)及び尖度γ2(g2):
μ 1 ( g 2 ) = − 6 n + 1 , μ 2 ( g 2 ) = 24 n ( n − 2 ) ( n − 3 ) ( n + 1 ) 2 ( n + 3 ) ( n + 5 ) , γ 1 ( g 2 ) ≡ μ 3 ( g 2 ) μ 2 ( g 2 ) 3 / 2 = 6 ( n 2 − 5 n + 2 ) ( n + 7 ) ( n + 9 ) 6 ( n + 3 ) ( n + 5 ) n ( n − 2 ) ( n − 3 ) , γ 2 ( g 2 ) ≡ μ 4 ( g 2 ) μ 2 ( g 2 ) 2 − 3 = 36 ( 15 n 6 − 36 n 5 − 628 n 4 + 982 n 3 + 5777 n 2 − 6402 n + 900 ) n ( n − 3 ) ( n − 2 ) ( n + 7 ) ( n + 9 ) ( n + 11 ) ( n + 13 ) .