第6章总体参数估计

1、简简 单单 随随 机机 抽抽 样样分分 层层 抽抽 样样整整 群群 抽抽 样样系系 统统 抽抽 样样多多 阶阶 段段 抽抽 样样概概 率率 抽抽 样样方方 便便 抽抽 样样判判 断断 抽抽 样样自自 愿愿 样样 本本滚滚 雪雪 球球 抽抽 样样配配 额额 抽抽 样样非非 概概 率率 抽抽 样样抽抽 样样 方方 式式Nn61234PPC222424PPCnnnNnN1x12x23x34x4 2.541044321N41iix61234C24xixi xp xpxx x xf f2服从,XNX2 2n,Nx2服从 1NnNn,Nx2服从 x xx xE En22x1NnNn22xNNnNn11N

2、N很很大大时时，可可近近似似为为nn22xxNn1n1NnNn1NnNn22xxx 0,1NnxxZ服从x 0,1N1NnNnxxZ服从x xxEnnS222x1NnNn1NnNnS222x1nin1i22xxsn nS Sn n2 22 2x xnSx2N Nn n1 1n nS S1 1N Nn nN Nn nS S1 1N Nn nN Nn nS S2 22 2x xx x 0,1NnSxxZ服从x 0,1N1NnNnSxxZ服从x XxxEnnS222x1NnNn1NnNnS222xnSnnS222xxNn1nS1NnNnS1NnNnS22xx n-1tnSxxt服从x n-1t1Nn

3、NnSxxt服从x N N1Nn11NnN趋近于1Nn11NnN也 趋趋近N NN N0 0N N1 1NN01-NNNNN01nn0n1pnpn0p1nnnnn01n np pn n0 0 pE n1pVar2p5 5n np p 5 5p p1 1n n n1,Npnp1pn1pnpn0 pE 1NnNn1pVar2p5 5n np p 5 5p p1 1n n 1NnNn1,Np 1NnNnp1p1NnNn1p5%Nn1NnNxps22 ExnnEEEnnExExxxxxxnn1.1.2121sn212222222222111111.211111nnnnnnnxxnEnnEExxxxxx

4、Snsn212222222222111111.211111nnnnnnnxxnEnnEExxxxxxSn,0nBnn0nEn0 10nVarn nnEnnEpEnn1100p2 222222211.1 nnnnEnnEExxxxSnSn21Plimin xEnxx xx x2 3xxx58. 2x65. 1xxx96. 158. 2xx xf0 xx58. 2x96. 1x65. 1x96. 1x65. 1122Z22 xf0 x221Z2Z2110. 065. 1645. 195. 02105. 02ZZZZZZ212Z221Z21xZ2xxXnx 1xxnNx2,1 , 0NnxZ1122

5、22nxnxPnxZPZZZnxnxZZ22nx ExnZZExx22 EExxxxNnnNnNnx11NnnNnNnZZZExx11222EExxxx4 .21x05. 0915. 0nx098. 005. 096. 12xxZEEExxxx0.09821.40.09821.421.49821.302xnxnxZZ22nsxnsxZZ2226x95. 0196. 12Z6 . 010610036nx176.16.096.12xxZEEExxxx176. 126176. 126176.27824.2488x10s01. 099. 0158. 2995. 0005. 0121005. 0201.

6、 02ZZZZZZ9129.012010nSnx355.29129.058.22xxZEEExxxx355. 288355. 288355.90645.851ntnSxt111.111111222222nSnxnSnxPnnSxnPntnPttttttnSxnSnxttn 1221nsxxxntE12NnnsNnNnsEx11NnnSnNnNnSnntttExx11111222EExxxx4851. 225126101. 001. 02tttn35x42s 3922. 0264nSx964. 03922. 04581. 212xxntEEExxxx964. 035964. 035964.350

7、36.34222230n30n30n30n30nnxZ212 NnNnxZnsxZ212NnNnsxZnsnxt12112NnNnsnxtnxZ212NnNnxZnsxZ212NnNnsxZn1,Np0,1Nn1ppZp5 5n np p 5 5p p1 1n nnppnp11p近似代替未知用样本总体nZZEpp122EEppppEEpppNNpNNnnppNnNnppp1111NnnppNnNnppZZZEpp1111222EEpppp%6510065 p0477. 010035. 065. 01nppp%59.30935. 00477. 096. 12或ppZE.%.35.74%65.55.%35. 9%65%35. 9%65.EEppppEnxZEx2EZZExxnn2222222212NnNnxZEx2222222222211ZEZZExxNNnNnNnNnNnN112222222ZEZxNNnx500Ex2865.27180000050096. 1222222EZxn285859.271800000110000180000010000196.150096.12222222222ZEZxNNn 28583.2718000001000018000001000096. 150096. 12222222222ZEZxNNnEZZEZ