1、 s uW9L !_蒋福坤null , 刘正春(嘉兴学院信息工程学院, 浙江嘉兴 314001)K1: 该文给出了指数分布参数的区间估计和假设检验的两种方法, 并通过数值计算进行了比较。1oM: 指数分布; 区间估计; 假设检验。 ms |: O212.1Abstract: T his paper expounds two methods, interval estimation and hypothetical test of parameterson indexdistribution, and makes comparison by means of numerical calculat
2、ion.Key words:index distribution ; interval estimation ; hypothesis test.CLC: O212.1DS M : A.cI|:1008- 6781(2004) 03- 0012- 030“ S/ 3?Z, d9F 0) s, X1, X 2,l, X n XB n“,“ (X-,Td9 nulln= nX-,nullsM1 V: 1d9 nulln= nX-V null, nnulls, M nullns f Pn(x )Pn(x) =01(n- 1)! nullnxn- 1e- nullxx 0) s, X 1, X2,l,
3、 X n XB“,d9 nulln= nullnX-V 1, nnulls,null(0, 1),nullns f null(x) V p, PPnullnull2 (n) 0) s,XB“X 1, X2,l, X n_L !H 0:null= null0|d9 nulln= null0nX-,L !H 0 H,nullnV 1, nnullsbA null,YV9 V: Pnullnullnullnull2 (n)= Pnullnull null1- null2 (n) = null2 “nullnull2 (n)null1- null2(n) , 0, nullnull2 (n)null1
4、- null2 (n) , +)b“ d9 nulln, nulln ,5 L !H 0;5, sH 0b1. 2 方法二1. 2. 1M1 !98VX null(null 0) s, X1, X 2,l, X n XB n“,:S=maxi X i, T = mini X i,5S+ T2 1nullB 9 b d9 1s V: 1= _ (S, T ) s f p(s, t)= n(n- 1)F(s)- F(t)n- 2p(s)p(t)00 0znull 0 z 0 H, F(z)= PZnull z= P U+ Vnullz= n(n- 1)z20 dvz- vv (e- v - e-
5、u) n- 2e- ue- vdu= nz20 (e- v - e- z+ v) n- 1e- vdv= nz20 n- 1k= 0( - 1) kCkn- 1e- kze- ( n- 2k) vdv= ne- n2z n- 1k= 0(- 1) kCkn- 12k - n + n n- 1k= 0( - 1) kCkn- 1n - 2k e- kz= (- 1) n+ 12 nn! (n - 12 )!8n- 12 e- n2z + n n- 1k= 0( - 1) kCkn- 1e- kzn - 2kznull0, F(z)= 0 H, b1. 2. 2 uW!98XV null( nul
6、l 0) s, X 1, X 2,l, X n XB n“,d9 Z=null(S+ T )sf F(z),null(0, 1),sf F(z) V p, PPz null2 (n) 0) s,XB“X 1, X2,l, X n_L !H 0:null= null0|d9 Z= null0(S+ T ),L ! H, Zsf F(z),A null,YV9 V PZnullz null2 (n)= PZnull z1- null2 (n) = null2 “z null2 (n)z1- null2 (n) , (0, z null2 (n)z1- null2 (n), +)b“4 d9 Z,
7、Z ,5 L !H 0;5, sH 0b1. 3 举例:X 0q P p V null sbCV |20q p k, /(:l H)10501100108012001300106010901080118013201250134010601150115012501310109011401160(1) p ( p 1null95% uWb(2)0q ( p V 1170l H(null= 0. 05)b:ZEB9 ( 1)X0q P p XV null s,“ n= 20,d9 null= nnullX-V1, 20nulls,1- null= 0. 95,null= 0. 05b9 , “nul
8、l0. 025(20)= 12. 22, null0. 975( 20) = 29.67,“4 x-= 1168, 98 ( p 1null95% uW ( 20116829. 67 , 20116812. 22 ) =(787, 1911)b(2)_L !H 0: 1null= 11170,null= 11170yn= 20,H 0 H,d9 null= 201170X-V 1, 20nullsbnull= 0. 05,9 “null0. 025( 20) = 12. 22, null0. 975(20) = 29. 67, 0, 12. 22 29. 67, +);“4X- =1168,d
9、9 nulln= 201170X-null= 233601170 = 19. 97null 0, 12. 22 29. 67, +), sL !H 0,0q ( p 1170l HbZE=9 ( 1) |“ n= 19,d9 Z= null(S+ T ),null= 0. 05 H,Zsf F(z) V “z0. 025(19)= 1. 777, z0. 975(19)= 6. 68,“4 -19 d9 ,9 z= 2390, 98 ( p 1null95% uW(23906. 68, 23901. 777)= (357. 78, 1344. 96)(2)_L !H 0: 1null= 1170 ( )b2 98V s uW9L !_ ZE,i 8 bYV9 1 , V AsYd9 null= nullnX-Z= null(S+ T ) 9 T s, “ ,s9? 3Mb987,d9 null= nullnX-rT1zd9 Z= null(S+ T )b ID: 1 B, +.l“ ( s uW9L !_ J . Ll M, 2002, ( 4) : 629j631. 2 B , C. d9M . Z: =Sv, 1990.(3 I )c14c嘉兴学院学报 第16卷第3期
