F-分布機率分布 / 維基百科,自由的 encyclopedia 在機率論和統計學裡,F-分布(F-distribution)是一種連續機率分布,[1][2][3][4]被廣泛應用於概似比率檢定,特別是ANOVA中。 Quick Facts 母數, 值域 ...F分布 機率密度函數 累積分布函數母數 d 1 > 0 , d 2 > 0 {\displaystyle d_{1}>0,\ d_{2}>0} 自由度值域 x ∈ [ 0 ; + ∞ ) {\displaystyle x\in [0;+\infty )\!} 機率密度函數 ( d 1 x ) d 1 d 2 d 2 ( d 1 x + d 2 ) d 1 + d 2 x B ( d 1 2 , d 2 2 ) {\displaystyle {\frac {\sqrt {\frac {(d_{1}\,x)^{d_{1}}\,\,d_{2}^{d_{2}}}{(d_{1}\,x+d_{2})^{d_{1}+d_{2}}}}}{x\,\mathrm {B} \!\left({\frac {d_{1}}{2}},{\frac {d_{2}}{2}}\right)}}\!} 累積分布函數 I d 1 x d 1 x + d 2 ( d 1 / 2 , d 2 / 2 ) {\displaystyle I_{\frac {d_{1}x}{d_{1}x+d_{2}}}(d_{1}/2,d_{2}/2)\!} 期望值 d 2 d 2 − 2 {\displaystyle {\frac {d_{2}}{d_{2}-2}}\!} for d 2 > 2 {\displaystyle d_{2}>2} 眾數 d 1 − 2 d 1 d 2 d 2 + 2 {\displaystyle {\frac {d_{1}-2}{d_{1}}}\;{\frac {d_{2}}{d_{2}+2}}\!} for d 1 > 2 {\displaystyle d_{1}>2} 變異數 2 d 2 2 ( d 1 + d 2 − 2 ) d 1 ( d 2 − 2 ) 2 ( d 2 − 4 ) {\displaystyle {\frac {2\,d_{2}^{2}\,(d_{1}+d_{2}-2)}{d_{1}(d_{2}-2)^{2}(d_{2}-4)}}\!} for d 2 > 4 {\displaystyle d_{2}>4} 偏度 ( 2 d 1 + d 2 − 2 ) 8 ( d 2 − 4 ) ( d 2 − 6 ) d 1 ( d 1 + d 2 − 2 ) {\displaystyle {\frac {(2d_{1}+d_{2}-2){\sqrt {8(d_{2}-4)}}}{(d_{2}-6){\sqrt {d_{1}(d_{1}+d_{2}-2)}}}}\!} for d 2 > 6 {\displaystyle d_{2}>6} 峰度 見下文Close
在機率論和統計學裡,F-分布(F-distribution)是一種連續機率分布,[1][2][3][4]被廣泛應用於概似比率檢定,特別是ANOVA中。 Quick Facts 母數, 值域 ...F分布 機率密度函數 累積分布函數母數 d 1 > 0 , d 2 > 0 {\displaystyle d_{1}>0,\ d_{2}>0} 自由度值域 x ∈ [ 0 ; + ∞ ) {\displaystyle x\in [0;+\infty )\!} 機率密度函數 ( d 1 x ) d 1 d 2 d 2 ( d 1 x + d 2 ) d 1 + d 2 x B ( d 1 2 , d 2 2 ) {\displaystyle {\frac {\sqrt {\frac {(d_{1}\,x)^{d_{1}}\,\,d_{2}^{d_{2}}}{(d_{1}\,x+d_{2})^{d_{1}+d_{2}}}}}{x\,\mathrm {B} \!\left({\frac {d_{1}}{2}},{\frac {d_{2}}{2}}\right)}}\!} 累積分布函數 I d 1 x d 1 x + d 2 ( d 1 / 2 , d 2 / 2 ) {\displaystyle I_{\frac {d_{1}x}{d_{1}x+d_{2}}}(d_{1}/2,d_{2}/2)\!} 期望值 d 2 d 2 − 2 {\displaystyle {\frac {d_{2}}{d_{2}-2}}\!} for d 2 > 2 {\displaystyle d_{2}>2} 眾數 d 1 − 2 d 1 d 2 d 2 + 2 {\displaystyle {\frac {d_{1}-2}{d_{1}}}\;{\frac {d_{2}}{d_{2}+2}}\!} for d 1 > 2 {\displaystyle d_{1}>2} 變異數 2 d 2 2 ( d 1 + d 2 − 2 ) d 1 ( d 2 − 2 ) 2 ( d 2 − 4 ) {\displaystyle {\frac {2\,d_{2}^{2}\,(d_{1}+d_{2}-2)}{d_{1}(d_{2}-2)^{2}(d_{2}-4)}}\!} for d 2 > 4 {\displaystyle d_{2}>4} 偏度 ( 2 d 1 + d 2 − 2 ) 8 ( d 2 − 4 ) ( d 2 − 6 ) d 1 ( d 1 + d 2 − 2 ) {\displaystyle {\frac {(2d_{1}+d_{2}-2){\sqrt {8(d_{2}-4)}}}{(d_{2}-6){\sqrt {d_{1}(d_{1}+d_{2}-2)}}}}\!} for d 2 > 6 {\displaystyle d_{2}>6} 峰度 見下文Close