均勻分布位置參數(shù)的估計(jì)量的漸近分布及應(yīng)用

熊加兵,朱成蓮

(淮陰師范學(xué)院數(shù)學(xué)系,江蘇淮安 223300)

均勻分布位置參數(shù)的估計(jì)量的漸近分布及應(yīng)用

熊加兵,朱成蓮

(淮陰師范學(xué)院數(shù)學(xué)系,江蘇淮安 223300)

對(duì)區(qū)間長(zhǎng)度為定值均勻分布位置參數(shù)的點(diǎn)估計(jì)量進(jìn)行了研究,得到位置參數(shù)點(diǎn)估計(jì)量的漸近分布.討論了漸近分布的相關(guān)性質(zhì).給出了位置參數(shù)的區(qū)間估計(jì)及其假設(shè)檢驗(yàn)方法.

均勻分布;漸近分布;統(tǒng)計(jì)量

1 引言

設(shè)隨機(jī)變量X服從區(qū)間[a,b]上的均勻分布,記X～U[a,b],其中未知參數(shù)a和b滿足?∞＜a＜b＜+∞,則X的密度函數(shù)為

2 相關(guān)引理

3 均勻分布位置參數(shù)估計(jì)量的漸近分布

由(4)式可以得到T的漸近密度所表示的曲線有如下性質(zhì).

定理3.2設(shè)(9)式所表示的曲線關(guān)于y軸對(duì)稱,以t軸為水平漸近線,在(?∞,0)上單調(diào)遞增、凸函數(shù),在(0,+∞)上單調(diào)遞減、凸函數(shù).

定理3.2的證明由分析知識(shí)易得.

4 應(yīng)用

[1]Adatia A.Estimation of quantiles of uniform distribution using generalized ranked set sampling[J].Park.J. Statist.,2004,20(3):355-368.

[2]陳光曙.關(guān)于均勻分布區(qū)間長(zhǎng)度的區(qū)間估計(jì)[J].純粹數(shù)學(xué)與應(yīng)用數(shù)學(xué),2006,22(3):349-354.

[3]潘高田,胡軍峰.小樣本的均勻分布參數(shù)的區(qū)間估計(jì)和假設(shè)檢驗(yàn)[J].數(shù)學(xué)的實(shí)踐與認(rèn)識(shí),2002,32(4):629-631.

[4]陳應(yīng)保,鄧昌松,李波.均勻分布區(qū)間中心的估計(jì)[J].華中師范大學(xué)學(xué)報(bào),2007,41(1):16-19.

Asymptotic distribution and application of estimation of the location parameter on uniform distribution

XIONG Jia-bing,ZHU Cheng-lian

(Mathematics Department of Huaiyin Teacher’s College,Huaian223300,China)

In this paper,estimation of the location parameter on uniform distribution is studied.The probability density function of asymptotic distribution have been given.The properties of the density function have been attained.The confidence interval of the location parameter,and the hypothetical test method have been given.

uniform distribution,asymptotic distribution,statistics

O211.1

A

1008-5513(2009)04-0677-04

2007-07-27.

江蘇省高校自然科學(xué)基金(05KJD110034).

熊加兵(1966-),副教授,研究方向：概率論與數(shù)理統(tǒng)計(jì).

2000MSC:62F10