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點推定에 대하여

Title
點推定에 대하여
Other Titles
On the point estimation
Authors
蔣美英
Issue Date
1983
Department/Major
교육대학원 수학교육전공
Keywords
점추정point estimation수학교육
Publisher
이화여자대학교 교육대학원
Degree
Master
Advisors
정영진
Abstract
本 硏究에서는 推測統計學의 가장 基本的인 母敎의 推定에서, 특히 推定量을 選擇하는 길잡이가 되는 重要한 性質인 不偏性, 一致性, 有效性, 充足性, 最尤性들의 性質을 밝히고, 特定한 母集團에서의 여러 가지 點推定量의 性質을 調査하여 다음과 같은 事實을 밝혔다. 二項分布, 正規分布, Poisson 分布에 따르는 母集團에서, 1) 標本平均은 母平均의 不偏, 一致, 有效, 充足, 最尤推定量이다. 2) 標本分散은 母分散의 不偏推定量이 아니다. (단, 正規母集團에서의 標本分散은 母分散의 最尤推定量이다.) 3) 母分散의 不偏推定量 σ^^(2)은 다음과 같다. σ^^(2) = (1)/(n-1)·□(x_(i) - X ̄)^(2) 4) 標本比率은 母比率의 不偏, 一致, 有效, 充足, 最尤推定量이다.;In this paper we study the desirable properties such as unbiasedness, consisteny, efficiency, sufficiency, maximum likelihoodness in the point estimation. Especially we prove the following; 1) The sample mean X ̄( X ̄=(1)/(n)·□X_(i)) is unbiased, consistent, efficient, sufficient and maximum likelihood estimator of mean of population μ. (According to theorem 1, 4, 5, 9, 11 and corollary 6, 9, 11) 2) Sample variance S^(2) (S^(2)=(1)/(n)·□(X_(i)-X ̄)^(2)) is not unbiased estimator of variance of population σ^(2). (In a random sample of a normal population, sample variance S^(2) is the maximum likelihood estimator of variance of population σ^(2).) 3) Unbiased estimator σ^(2) of variance of population σ^(2) is as follows, σ^(2)=(n·S^(2))/(n-1)=(1)/(n-1)·□(X_(i)-X ̄)^(2) (According to theorem 3) 4) The proportion of the sample P ̄(P ̄=(X)/(n)) is unbiased, consistent, efficient, sufficient, and maximum likelihood estimator of proportion of population p. (According to corollary 1, 4 and theorem 6, 8, 10)
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교육대학원 > 수학교육전공 > Theses_Master
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