8 M' `( `7 X. u! H* Q V' D" i. Y! N/ ] 0 g- g% A4 M9 M" g3 j1 u- k2、负二项分布5 v, @* r: a4 K; x
– 矩母函数:M ( t ) = ( 1 − p ) r ( 1 − p e t ) − r M(t) = (1-p)^r(1-pe^t)^{-r}M(t)=(1−p) ' A: e8 J" y) ~5 |1 t. c5 O, s& _1 i
r 1 D. T" w1 d' i6 _/ ?% ?1 r; k. p (1−pe & ]/ _# f8 _/ t; a& B/ |: z! p c
t 5 Z1 ?( A2 f! u% k5 _5 [8 |& } ) 8 }+ Y. }, j# ~+ u( w& \2 x4 U. l3 j
−r , V* h2 G; y; d" S# O / f( c. p" K3 ]1 L
! [8 l; J. |9 |7 r- J/ M ' @+ z9 M$ k9 O& g/ y: m– 偏度:S k e w ( X ) = n 3 + 3 n 2 + 2 n − ( 3 n 2 + 3 n ) p + n p 2 ( n 2 + n ( 1 − p ) ) 3 / 2 Skew(X) = \frac{n^3+3n^2+2n-(3n^2+3n)p+np^2}{(n^2+n(1-p))^{3/2}}Skew(X)= ! L( e% o& I- u9 g(n + U3 U8 O4 r! h0 J+ }2- f' }. t( S( H5 f) e2 x
+n(1−p)) $ \0 O- H% h9 |4 {( K3 e" O3/2, j/ _9 j/ S3 w, E0 n8 L
4 G) _0 x& w# F
n . T. V( ?: a9 x
3 8 y7 B d) i( Q4 j3 A+ e +3n * l4 z! L" N* q0 s
2. T; @) y: G6 p& `2 {" o5 I
+2n−(3n , A2 j. x. o9 U Y
20 q! r; [) o T* G3 N$ `8 i. E
+3n)p+np . N7 t0 v7 L! F2$ j" _2 G* A/ e' N5 h. M
: t. X* q9 r6 p: d( c" [% ] # n! E* r% u. L7 D) p7 J2 s' A8 ]' o9 B 1 h& z2 H* n; l
2 Y- c4 h$ E8 E) r ]( u; o# H
* |, L$ N" a: X3 i1 g$ h
– 峰度:k u r t ( X ) = 略 kurt(X) = 略kurt(X)=略 (带入递推公式自行运算)# Y. I) L2 u. A1 ^3 r0 o