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來源資料
頁籤選單縮合
題 名 | 非常態性資料對樣本中位數之影響=Effect of Non-Normality on the Sample Median |
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作 者 | 周昭宇; 蕭武夫; | 書刊名 | 科技學刊 |
卷 期 | 7:3 1998.07[民87.07] |
頁 次 | 頁271-278 |
分類號 | 440 |
關鍵詞 | 中位數; Burr分配; 非常態性; 偏態; 峰態; Median; Burr distribution; Non-normality; Skewness; Kurtosis; |
語 文 | 中文(Chinese) |
中文摘要 | 當資料型態為對稱或近似對稱分配時,我們通常以平均數來測量這些資料的中央 位置(location)。而當資料為非對稱分配時,由於會受到極端值的影響,所以相對於平均數 而言,中位數是一個對極端值不敏感之測量位置的替代方案。本文利用Burr 分配來研究非 常態性對樣本中位數的影響。由研究的結果可得到以下四點結論:(1)當母體分配為適度的 右偏或為高狹峰時,樣本中位數的期望值會比母體平均數小;(2)當母體分配為極度的右偏 時,樣本中位數的有效性會比樣本平均數高;(3)當母體之偏態係數增加時,樣本中位數之 偏態係數亦隨之增加。而母體之峰態係數對樣本中位數之偏態係數沒有影響;(4)當母體之 偏態係數增加時,樣本中位數之峰態係數會隨之減少。當母體之峰態係數增加時,樣本中位 數之峰態係數亦隨之增加。 |
英文摘要 | The most popular measure of location is the mean, especially when the data are symmetrically or nearly symmetrically distributed. For asymmetrical distributions, the median is a good alternative measure of location and is often preferred to the mean, which is adversely influenced by outliers. In this article, the Burr distribution is used to study the effect of non-normality on the sample median. From the results of study, the following conclusions can be drawn: (1) The expected value of sample median will be less than the population mean as the underlying distribution is moderately positive skewed or leptokurtic; (2) As the underlying distribution is extremely positive skewed, the sample median is more efficient than the sample mean; (3) As the coefficient of skewness of population increases, the coefficient of skewness of sample median also increases. The value of the coefficient of kurtosis for population seems to have no effect on the coefficient of skewness of sample median; (4) As the coefficient of skewness of population increases, the coefficient of kurtosis of sample median decreases. As the coefficient of kurtosis of population increases, the coefficient of kurtosis of sample median also increases. |
本系統中英文摘要資訊取自各篇刊載內容。